This document provides advice on practical techniques related to the creation of content in HTML that is language aware. This is a W3C Draft produced by the Internationalization Working Group, part of the W3C Internationalization Activity. The Working Group expects to advance this Working Draft to Working Group Note. Please send comments on this document to<EMAIL_ADDRESS>(publicly archived).
All authors and producers of HTML and CSS.
This document provides guidance for developers of HTML that enables support for international deployment. Enabling international deployment is the responsibility of all content authors, not just localization groups or vendors, and is relevant from the very start of development.
It is assumed that readers of this document are proficient in developing HTML and XHTML pages - this document is limited to providing advice specifically related to internationalization.
This document lists a number of do's and don'ts, which we will refer to as techniques, related to authoring pages in right-to-left scripts. Each technique is followed by a 'detail' link which provides further information. Where needed, you can get additional information and explanations by following the links to the appropriate section of the techniques index, listed alongside each section.
If a technique says 'consider', there are usually pros and cons involved in following the advice given, and you should follow the link to more detailed information to be sure you understand these. In some cases it may be that not all browsers support the features described. In other cases, it may be purely up to you to decide whether or not this is a good idea.
Applications already exist that can use information about the natural language (ie. the human, non-programmatic language) of content to deliver to users the most relevant information or styling, based on their language preferences. The more content is tagged and tagged correctly, the more useful and pervasive such applications will become.
Language information is useful for things such as authoring tools, translation tools, accessibility, font selection, page rendering, search, and scripting.
These applications can't work, however, if the information about the language of the text is not available. Language information should therefore be specified for the page as a whole, and wherever language changes within the page.
In the future there will be other applications for language information, driven by developments in technology. For example, implementations of the CSS3 :first-letter
pseudo-element will need language information to apply correct styling. However, we are currently faced with a circular problem. People who don't see the application of language information do not provide information about their content, and language-related applications are slow to be deployed until this information is widely available. This cycle can be broken by content authors taking steps now to declare language information. This is usually very easy to do, and carries no penalties, and it is gradually beginning to happen.
Metadata that describes the language of the intended audience is about the document as a whole. Such metadata may be used for searching, serving the right language version, classification, etc. Where there are language changes in a document, information about the language of the intended audience is not specific enough to support text-processing, that is to say, in a way that would be needed for the application of text-to-speech, styling, automatic font assignment, etc.
The language of the intended audience does not include every language used in a document. Many documents on the Web contain embedded fragments of content in different languages, whereas the page is clearly aimed at speakers of one particular language. For example, a German city-guide for Beijing may contain useful phrases in Chinese, but it is aimed at a German-speaking audience, not a Chinese one.
On the other hand, it is also possible to imagine a situation where a document contains the same or parallel content in more than one language. For example, a Web page may welcome Canadian readers with French content in the left column, and the same content in English in the right-hand column. Here the document is equally targeted at speakers of both languages, so there are two audience languages. This situation is not as common on the Web as in printed material since it is easy to link to separate pages on the Web for different audiences, but it does occur where there are multilingual communities. Another use case is a blog or a news page aimed at a multilingual community, where some articles on a page are in one language and some in another.
There are also pages where the navigational information, including the page title, is in one language but the real content of the page is in another. While this is not necessarily good practice, it doesn't change the fact that the language of the intended audience is usually that of the content, regardless of the language at the top of the document source.
Metadata about the language of the intended audience is usually best declared outside the document in the HTTP Content-Language
header.
When specifying the text-processing language you are declaring the language in which a specific range of text is actually written, so that user agents or applications that manipulate the text, such as voice browsers, spell checkers, or style processors can effectively handle the text in question. So we are, by necessity, talking about associating a single language with a specific range of text.
This specificity distinguishes the declaration of the language for text-processing from the language of the intended audience.
The language for text-processing is usually best declared using attributes on elements, including the html
element, which contains all the content of the document. Enclosed elements inherit the declared value, but you can, of course, override an initial declaration by specifying a different language on embedded elements where the language changes, eg. a French word in an English paragraph.
There are separate mechanisms for declaring character encoding and directionality in HTML, and these ideas should not be confused with mechanisms for declaring language.
Character encoding refers to the sequences of bytes that are used to represent characters in text. It is important to declare which encoding is being used for your document, but this is a separate issue from declaring language. (To better understand character encoding declarations see Handling character encodings in HTML and CSS.)
Some people think that information about language can be inferred from the character encoding, but this is not true. There would have to be a one-to-one mapping between encoding and language for this to work, and there isn't. A single character encoding such as ISO 8859-1 (Latin1), could encode both French and English, as well as a great many other languages. In addition, different character encodings can be used for a single language, eg, Arabic could be encoded with 'Windows-1256' or 'ISO 8859-6' or 'UTF-8'.
Nowadays, this argument should be moot anyway, because content authors should always use UTF-8 as the character encoding. Since UTF-8 encodings cover all but the rarest of language use with a single encoding, there is normally no need to match language and encoding.
Text direction is another thing that should not be confused with language. In some scripts, such as Arabic and Hebrew, displayed text is read predominantly from right to left, although within that flow, numbers and text from other scripts are displayed from left to right. Markup is needed to set the overall right-to-left context, and in some circumstances markup is needed to correctly render bidirectional text, but this cannot necessarily be done using language markup. (To better understand text direction and markup see Creating HTML Pages in Arabic, Hebrew and Other Right-to-left Scripts.)
As with encodings and language, there is not always a one-to-one mapping between language and script, and therefore
directionality. For example, Azerbaijani can be written using both right-to-left and left-to-right scripts, and the language code az
can be relevant for either. In addition, text direction markup used with inline text applies a range of different values to the text, whereas language is a simple switch that is not up to the tasks required.
Always declare the default language for text in the page using attributes on the html
tag, unless the document contains content aimed at speakers of more than one language. detail
Do NOT use the meta
element with the content
attribute set to Content-Language
. detail
Use language attributes rather than HTTP to declare the default language for text processing. detail
Do not declare the default language of a document in the body
element, use the html
element. detail
Use the lang
attribute for pages served as HTML, and the xml:lang
attribute for pages served as XML. For XHTML 1.x and HTML5 polyglot documents, use both together. detail
Learn more about:
Use the lang
and/or xml:lang
attributes around text to indicate any changes in language. detail
Use the lang
attribute for pages served as HTML, and the xml:lang
attribute for pages served as XML. For XHTML 1.x and HTML5 polyglot documents, use both together. detail
If the text in attribute values and element content is in different languages, consider using a nested approach. detail
Learn more about:
Use subtags as defined by BCP 47 for language attribute values. detail Use the shortest possible language tag values. detail
Where possible, use the codes zh-Hans
and zh-Hant
to refer to Simplified and Traditional Chinese, respectively. detail
Use the subtag zxx
when the text is known to be not in any language. detail
If using XML, and the format you are using supports it, use xml:lang=""
, otherwise use xml:lang="und"
when the language is undetermined and you have to label it. detail
Learn more about:
Consider using a Content-Language
HTTP header to declare metadata about the language(s) of the intended audience of a document. detail
Where a document contains content aimed at speakers of more than one language, use the HTTP Content-Language
header with a comma-separated list of language tags. detail
Learn more about:
When pointing to a resource in another language, consider the pros and cons before indicating the language of the target document. detail
If you want to indicate that the target document of an a
element is in another language, consider the pros and cons before using hreflang
with CSS. detail
Do not use flag icons to indicate languages. detail
Learn more about:
This Editor's Draft has been changed as follows:
Members of the Internationalization Working Group and former GEO Working Group have contributed their time and valuable comments to shaping these guidelines.


RT @HeyNickMurphy: 2014 Me: “In Winter Soldier, I don’t see how Hydra/Nazis could infiltrate the government without anyone noticing.”
2017…


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--- layout: default title: Sam Loves Coffee permalink: / exclude: true --- {% include landing.html %}


Watching @garybernhardt write a text editor... way better use of my time than the debate. https://www.twitch.tv/gary_bernhardt/v/90796516?t=11m57s
10/20/2016, 12:00:02 AM
Favs: 1
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link--- layout: tweet ---
Watching @garybernhardt write a text editor... way better use of my time than the debate. https://www.twitch.tv/gary_bernhardt/v/90796516?t=11m57s
10/20/2016, 12:00:02 AM
Favs: 1
Retweets: 0
link


BitmovinApiSdk\Models\LevelH264
Synopsis
class LevelH264
extends Enum
{
- // methods
- public static LevelH264 create()
- public static LevelH264 L1()
- public static LevelH264 L1b()
- public static LevelH264 L1_1()
- public static LevelH264 L1_2()
- public static LevelH264 L1_3()
- public static LevelH264 L2()
- public static LevelH264 L2_1()
- public static LevelH264 L2_2()
- public static LevelH264 L3()
- public static LevelH264 L3_1()
- public static LevelH264 L3_2()
- public static LevelH264 L4()
- public static LevelH264 L4_1()
- public static LevelH264 L4_2()
- public static LevelH264 L5()
- public static LevelH264 L5_1()
- public static LevelH264 L5_2()
- // Inherited methods from Enum
- public void __construct()
- public mixed getValue()
- public mixed getKey()
- public string __toString()
- public final bool equals()
- public static array keys()
- public static array values()
- public static array toArray()
- public static bool isValidKey()
- public static mixed search()
- public static LevelH264 __callStatic()
- public mixed jsonSerialize()
Hierarchy
Extends
Methods
public
- L1() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L1_1() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L1_2() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L1_3() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L1b() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L2() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L2_1() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L2_2() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L3() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L3_1() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L3_2() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L4() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L4_1() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L4_2() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L5() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L5_1() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- L5_2() — Specified set of constraints that indicate a degree of required decoder performance for a profile, see: https://en.wikipedia.org/wiki/H.264/MPEG-4_AVC#Levels
- create()
Inherited from BitmovinApiSdk\Common\Enum
public
- __callStatic() — Returns a value when called statically like so: MyEnum::SOME_VALUE() given SOME_VALUE is a class constant
- __toString()
- equals() — Determines if Enum should be considered equal with the variable passed as a parameter.
- getKey() — Returns the enum key (i.e. the constant name).
- getValue()
- isValidKey() — Check if is valid enum key
- jsonSerialize() — Specify data which should be serialized to JSON. This method returns data that can be serialized by json_encode() natively.
- keys() — Returns the names (keys) of all constants in the Enum class
- search() — Return key for value
- toArray() — Returns all possible values as an array
- values() — Returns instances of the Enum class of all Enum constants


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Last updated 29 January 2020
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In Conversation: Steve Lieberman [CEO of SJ Lighting]
"And that's what it takes. That's what separates, you know, the pros from the amateurs..."
by KaneWelcome to In Conversation, the podcast dedicated to giving you an unparalleled look into electronic music's greatest minds, both in the studio and beyond. We deconstruct their daily routines, fears, and quirks, showing you what makes them tick, and what exactly makes them so successful. From artists to managers, agents and promoters, these are the people who make it happen, pushing our community forward.
Have you ever been to a club in Los Angeles, Las Vegas, Miami, or New York? What about festivals like EDC or Coachella? If so, have you ever taken a moment to stop and really look at the stages, screens, lasers, and lighting? These are things that we enjoy but often take for granted, as they are to enhance the performance of the artists playing on stage and overall experience. But what exactly goes into designing these? How does a stage as massive as Circuit Grounds at EDC Las Vegas go from idea to finished product? If you've ever wondered, our guest today is the man behind it all.
Meet Steve Lieberman, founder of SJ Lighting. He and his company have become one of, if not the top stage and lighting designers for the country's biggest clubs and festivals, and his resume is nothing short of mind-boggling. In fact, he's responsible for most of the top clubs in LA and Las Vegas. In this chat, we discuss his founding of SJ Lighting, how he got involved in such projects like Insomniac festivals and Coachella, and what it takes to create a lasting impression with your work.
Special thanks to our sponsors LANDR and Rode Mics for helping make this podcast possible.


{% extends "base.html" %} {% set active_item = "index" %} {% block description %}Renzo Lucioni's personal website, portfolio, and writings, often about data visualization and software development.{% endblock description %} {% block content %}


Unannounced game from Capcom will be playable on December 21st at Jump Fiesta 2020
by John PapadopoulosAn unannounced game from Capcom will be playable at this year’s Jump Fiesta event. This event begins on December 21st and ends on December 22nd. Moreover, this event is after The Video Games Awards 2019, in which Capcom may reveal Resident Evil 3 Remake.
Do note that the RE3 Remake announcement at the VGA2019 is mere speculation and nothing more at this point. We’ve heard from a lot of sources that Capcom targets a 2020/2021 release, so it would make sense to announce the game during this event.
The other Capcom games that will be playable at Jump Fiesta 2020 are: Mega Man Zero/ZX Legacy Collection and Monster Hunter World: Iceborne. Surprisingly enough, the Resident Evil multiplayer spin-off game may not be playable at Jump Fiesta 2020.
We’ll be sure to keep you posted, so stay tuned for more!
Thanks Ryokutya2089


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If you have any questions or comments, please feel free to contact us, we will be happy to help you.
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cqparts_gears package¶
Submodules¶
cqparts_gears.base module¶
-
class
cqparts_gears.base.
Gear
(*largs, **kwargs)¶ Bases:
cqparts.part.Part
ParametricObject
constructor parameters:Parameters: -
make_simple
()¶
-
cqparts_gears.trapezoidal module¶
-
class
cqparts_gears.trapezoidal.
TrapezoidalGear
(*largs, **kwargs)¶ Bases:
cqparts_gears.base.Gear
ParametricObject
constructor parameters:Parameters: - effective_radius (
float
) – designed equivalent wheel radius - face_angle (
float
) – angle of tooth edge radial edge (unit: degrees) - flat_top (
bool
) – ifTrue
the tops of teeth are flat - spacing_ratio (
float
) – tooth thickness as a ratio of the distance between them - tooth_count (
int
) – number of teeth - tooth_height (
float
) – radial height of teeth - width (
float
) – gear thickness
Basic gear with trapezoidal tooth shape.
-
initialize_parameters
()¶
-
make
()¶
-
mate_bottom
¶
-
mate_top
¶
- effective_radius (
Module contents¶
Copyright 2018 Peter Boin
Licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except in compliance with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.


Ken Wright, founder of Wright Design is an accomplished innovator with over twenty years of extensive experience in product and technology development. Mr. Wright has an accomplished track record in both developing and bringing to market pioneering innovations in both the medical and consumer industries. Ken developed the original air drives ear phones, Eclipse breast monitoring devices, and provided technical guidance to the development of the movie Titanic.


|
ReactPhysics3D
0.7.1
Physics engine library
|
This class represents a rigid body of the physics engine. More...
#include <RigidBody.h>
Public Member Functions | |
| RigidBody (const Transform &transform, CollisionWorld &world, bodyindex id) | |
| Constructor. More... | |
| virtual | ~RigidBody () override |
| Destructor. | |
| RigidBody (const RigidBody &body)=delete | |
| Deleted copy-constructor. | |
| RigidBody & | operator= (const RigidBody &body)=delete |
| Deleted assignment operator. | |
| void | setType (BodyType type) |
| Set the type of the body (static, kinematic or dynamic) More... | |
| virtual void | setTransform (const Transform &transform) override |
| Set the current position and orientation. More... | |
| decimal | getMass () const |
| Return the mass of the body. More... | |
| Vector3 | getLinearVelocity () const |
| Return the linear velocity. More... | |
| void | setLinearVelocity (const Vector3 &linearVelocity) |
| Set the linear velocity of the body. More... | |
| Vector3 | getAngularVelocity () const |
| Return the angular velocity. More... | |
| void | setAngularVelocity (const Vector3 &angularVelocity) |
| Set the angular velocity. More... | |
| virtual void | setIsSleeping (bool isSleeping) override |
| Set the variable to know whether or not the body is sleeping. | |
| void | setInertiaTensorLocal (const Matrix3x3 &inertiaTensorLocal) |
| Set the local inertia tensor of the body (in body coordinates) More... | |
| void | setInverseInertiaTensorLocal (const Matrix3x3 &inverseInertiaTensorLocal) |
| Set the inverse local inertia tensor of the body (in body coordinates) More... | |
| const Matrix3x3 & | getInverseInertiaTensorLocal () const |
| Get the inverse local inertia tensor of the body (in body coordinates) | |
| Matrix3x3 | getInertiaTensorInverseWorld () const |
| Return the inverse of the inertia tensor in world coordinates. More... | |
| void | setCenterOfMassLocal (const Vector3 ¢erOfMassLocal) |
| Set the local center of mass of the body (in local-space coordinates) More... | |
| void | setMass (decimal mass) |
| Set the mass of the rigid body. More... | |
| bool | isGravityEnabled () const |
| Return true if the gravity needs to be applied to this rigid body. More... | |
| void | enableGravity (bool isEnabled) |
| Set the variable to know if the gravity is applied to this rigid body. More... | |
| Material & | getMaterial () |
| Return a reference to the material properties of the rigid body. More... | |
| void | setMaterial (const Material &material) |
| Set a new material for this rigid body. More... | |
| decimal | getLinearDamping () const |
| Return the linear velocity damping factor. More... | |
| void | setLinearDamping (decimal linearDamping) |
| Set the linear damping factor. More... | |
| decimal | getAngularDamping () const |
| Return the angular velocity damping factor. More... | |
| void | setAngularDamping (decimal angularDamping) |
| Set the angular damping factor. More... | |
| const JointListElement * | getJointsList () const |
| Return the first element of the linked list of joints involving this body. More... | |
| JointListElement * | getJointsList () |
| Return the first element of the linked list of joints involving this body. More... | |
| void | applyForceToCenterOfMass (const Vector3 &force) |
| Apply an external force to the body at its center of mass. More... | |
| void | applyForce (const Vector3 &force, const Vector3 &point) |
| Apply an external force to the body at a given point (in world-space coordinates). More... | |
| void | applyTorque (const Vector3 &torque) |
| Apply an external torque to the body. More... | |
| virtual ProxyShape * | addCollisionShape (CollisionShape *collisionShape, const Transform &transform, decimal mass) |
| Add a collision shape to the body. More... | |
| virtual void | removeCollisionShape (const ProxyShape *proxyShape) override |
| Remove a collision shape from the body. More... | |
| void | recomputeMassInformation () |
| Recompute the center of mass, total mass and inertia tensor of the body using all the collision shapes attached to the body. More... | |
| Public Member Functions inherited from reactphysics3d::CollisionBody | |
| CollisionBody (const Transform &transform, CollisionWorld &world, bodyindex id) | |
| Constructor. More... | |
| virtual | ~CollisionBody () override |
| Destructor. | |
| CollisionBody (const CollisionBody &body)=delete | |
| Deleted copy-constructor. | |
| CollisionBody & | operator= (const CollisionBody &body)=delete |
| Deleted assignment operator. | |
| BodyType | getType () const |
| Return the type of the body. More... | |
| void | setType (BodyType type) |
| Set the type of the body. More... | |
| virtual void | setIsActive (bool isActive) override |
| Set whether or not the body is active. More... | |
| const Transform & | getTransform () const |
| Return the current position and orientation. More... | |
| virtual ProxyShape * | addCollisionShape (CollisionShape *collisionShape, const Transform &transform) |
| Add a collision shape to the body. More... | |
| const ContactManifoldListElement * | getContactManifoldsList () const |
| Return the first element of the linked list of contact manifolds involving this body. More... | |
| bool | testPointInside (const Vector3 &worldPoint) const |
| Return true if a point is inside the collision body. More... | |
| bool | raycast (const Ray &ray, RaycastInfo &raycastInfo) |
| Raycast method with feedback information. More... | |
| bool | testAABBOverlap (const AABB &worldAABB) const |
| Test if the collision body overlaps with a given AABB. More... | |
| AABB | getAABB () const |
| Compute and return the AABB of the body by merging all proxy shapes AABBs. More... | |
| ProxyShape * | getProxyShapesList () |
| Return the linked list of proxy shapes of that body. More... | |
| const ProxyShape * | getProxyShapesList () const |
| Return the linked list of proxy shapes of that body. More... | |
| Vector3 | getWorldPoint (const Vector3 &localPoint) const |
| Return the world-space coordinates of a point given the local-space coordinates of the body. More... | |
| Vector3 | getWorldVector (const Vector3 &localVector) const |
| Return the world-space vector of a vector given in local-space coordinates of the body. More... | |
| Vector3 | getLocalPoint (const Vector3 &worldPoint) const |
| Return the body local-space coordinates of a point given in the world-space coordinates. More... | |
| Vector3 | getLocalVector (const Vector3 &worldVector) const |
| Return the body local-space coordinates of a vector given in the world-space coordinates. More... | |
| Public Member Functions inherited from reactphysics3d::Body | |
| Body (bodyindex id) | |
| Constructor. More... | |
| Body (const Body &body)=delete | |
| Deleted copy-constructor. | |
| Body & | operator= (const Body &body)=delete |
| Deleted assignment operator. | |
| virtual | ~Body ()=default |
| Destructor. | |
| bodyindex | getId () const |
| Return the ID of the body. More... | |
| bool | isAllowedToSleep () const |
| Return whether or not the body is allowed to sleep. More... | |
| void | setIsAllowedToSleep (bool isAllowedToSleep) |
| Set whether or not the body is allowed to go to sleep. More... | |
| bool | isSleeping () const |
| Return whether or not the body is sleeping. More... | |
| bool | isActive () const |
| Return true if the body is active. More... | |
| void * | getUserData () const |
| Return a pointer to the user data attached to this body. More... | |
| void | setUserData (void *userData) |
| Attach user data to this body. More... | |
| bool | operator< (const Body &body2) const |
| Smaller than operator. | |
| bool | operator> (const Body &body2) const |
| Larger than operator. | |
| bool | operator== (const Body &body2) const |
| Equal operator. | |
| bool | operator!= (const Body &body2) const |
| Not equal operator. | |
Protected Member Functions | |
| void | removeJointFromJointsList (reactphysics3d::MemoryManager &memoryManager, const Joint *joint) |
| Remove a joint from the joints list. | |
| void | updateTransformWithCenterOfMass () |
| Update the transform of the body after a change of the center of mass. | |
| virtual void | updateBroadPhaseState () const override |
| Update the broad-phase state for this body (because it has moved for instance) | |
| void | updateInertiaTensorInverseWorld () |
| Update the world inverse inertia tensor of the body. More... | |
| Protected Member Functions inherited from reactphysics3d::CollisionBody | |
| void | resetContactManifoldsList () |
| Reset the contact manifold lists. | |
| void | removeAllCollisionShapes () |
| Remove all the collision shapes. | |
| void | updateProxyShapeInBroadPhase (ProxyShape *proxyShape, bool forceReinsert=false) const |
| Update the broad-phase state of a proxy collision shape of the body. | |
| void | askForBroadPhaseCollisionCheck () const |
| Ask the broad-phase to test again the collision shapes of the body for collision (as if the body has moved). More... | |
| int | resetIsAlreadyInIslandAndCountManifolds () |
| Reset the mIsAlreadyInIsland variable of the body and contact manifolds. More... | |
Protected Attributes | |
| decimal | mInitMass |
| Intial mass of the body. | |
| Vector3 | mCenterOfMassLocal |
| Center of mass of the body in local-space coordinates. More... | |
| Vector3 | mCenterOfMassWorld |
| Center of mass of the body in world-space coordinates. | |
| Vector3 | mLinearVelocity |
| Linear velocity of the body. | |
| Vector3 | mAngularVelocity |
| Angular velocity of the body. | |
| Vector3 | mExternalForce |
| Current external force on the body. | |
| Vector3 | mExternalTorque |
| Current external torque on the body. | |
| Matrix3x3 | mUserInertiaTensorLocalInverse |
| Inverse Local inertia tensor of the body (in local-space) set by the user with respect to the center of mass of the body. | |
| Matrix3x3 | mInertiaTensorLocalInverse |
| Inverse of the inertia tensor of the body. | |
| Matrix3x3 | mInertiaTensorInverseWorld |
| Inverse of the world inertia tensor of the body. | |
| decimal | mMassInverse |
| Inverse of the mass of the body. | |
| bool | mIsGravityEnabled |
| True if the gravity needs to be applied to this rigid body. | |
| Material | mMaterial |
| Material properties of the rigid body. | |
| decimal | mLinearDamping |
| Linear velocity damping factor. | |
| decimal | mAngularDamping |
| Angular velocity damping factor. | |
| JointListElement * | mJointsList |
| First element of the linked list of joints involving this body. | |
| bool | mIsCenterOfMassSetByUser |
| True if the center of mass is set by the user. | |
| bool | mIsInertiaTensorSetByUser |
| True if the inertia tensor is set by the user. | |
| Protected Attributes inherited from reactphysics3d::CollisionBody | |
| BodyType | mType |
| Type of body (static, kinematic or dynamic) | |
| Transform | mTransform |
| Position and orientation of the body. | |
| ProxyShape * | mProxyCollisionShapes |
| First element of the linked list of proxy collision shapes of this body. | |
| uint | mNbCollisionShapes |
| Number of collision shapes. | |
| ContactManifoldListElement * | mContactManifoldsList |
| First element of the linked list of contact manifolds involving this body. | |
| CollisionWorld & | mWorld |
| Reference to the world the body belongs to. | |
| Protected Attributes inherited from reactphysics3d::Body | |
| bodyindex | mID |
| ID of the body. | |
| bool | mIsAlreadyInIsland |
| True if the body has already been added in an island (for sleeping technique) | |
| bool | mIsAllowedToSleep |
| True if the body is allowed to go to sleep for better efficiency. | |
| bool | mIsActive |
| True if the body is active. More... | |
| bool | mIsSleeping |
| True if the body is sleeping (for sleeping technique) | |
| decimal | mSleepTime |
| Elapsed time since the body velocity was bellow the sleep velocity. | |
| void * | mUserData |
| Pointer that can be used to attach user data to the body. | |
Friends | |
| class | DynamicsWorld |
| class | ContactSolver |
| class | BallAndSocketJoint |
| class | SliderJoint |
| class | HingeJoint |
| class | FixedJoint |
This class represents a rigid body of the physics engine.
A rigid body is a non-deformable body that has a constant mass. This class inherits from the CollisionBody class.
| RigidBody::RigidBody | ( | const Transform & | transform, |
| CollisionWorld & | world, | ||
| bodyindex | id | ||
| ) |
Constructor.
| transform | The transformation of the body |
| world | The world where the body has been added |
| id | The ID of the body |
|
virtual |
Add a collision shape to the body.
When you add a collision shape to the body, an internal copy of this collision shape will be created internally.
Therefore, you can delete it right after calling this method or use it later to add it to another body. This method will return a pointer to a new proxy shape. A proxy shape is an object that links a collision shape and a given body. You can use the returned proxy shape to get and set information about the corresponding collision shape for that body.
| collisionShape | The collision shape you want to add to the body |
| transform | The transformation of the collision shape that transforms the local-space of the collision shape into the local-space of the body |
| mass | Mass (in kilograms) of the collision shape you want to add |
Apply an external force to the body at a given point (in world-space coordinates).
If the point is not at the center of mass of the body, it will also generate some torque and therefore, change the angular velocity of the body.
If the body is sleeping, calling this method will wake it up. Note that the force will we added to the sum of the applied forces and that this sum will be reset to zero at the end of each call of the DynamicsWorld::update() method. You can only apply a force to a dynamic body otherwise, this method will do nothing.
| force | The force to apply on the body |
| point | The point where the force is applied (in world-space coordinates) |
|
inline |
Apply an external force to the body at its center of mass.
If the body is sleeping, calling this method will wake it up.
Note that the force will we added to the sum of the applied forces and that this sum will be reset to zero at the end of each call of the DynamicsWorld::update() method. You can only apply a force to a dynamic body otherwise, this method will do nothing.
| force | The external force to apply on the center of mass of the body |
|
inline |
Apply an external torque to the body.
If the body is sleeping, calling this method will wake it up.
Note that the force will we added to the sum of the applied torques and that this sum will be reset to zero at the end of each call of the DynamicsWorld::update() method. You can only apply a force to a dynamic body otherwise, this method will do nothing.
| torque | The external torque to apply on the body |
| void RigidBody::enableGravity | ( | bool | isEnabled | ) |
Set the variable to know if the gravity is applied to this rigid body.
| isEnabled | True if you want the gravity to be applied to this body |
|
inline |
Return the angular velocity damping factor.
|
inline |
Return the angular velocity.
|
inline |
Return the inverse of the inertia tensor in world coordinates.
The inertia tensor I_w in world coordinates is computed with the local inverse inertia tensor I_b^-1 in body coordinates by I_w = R * I_b^-1 * R^T where R is the rotation matrix (and R^T its transpose) of the current orientation quaternion of the body.
|
inline |
Return the first element of the linked list of joints involving this body.
|
inline |
Return the first element of the linked list of joints involving this body.
|
inline |
Return the linear velocity damping factor.
|
inline |
Return the linear velocity.
|
inline |
Return the mass of the body.
|
inline |
Return a reference to the material properties of the rigid body.
|
inline |
Return true if the gravity needs to be applied to this rigid body.
| void RigidBody::recomputeMassInformation | ( | ) |
Recompute the center of mass, total mass and inertia tensor of the body using all the collision shapes attached to the body.
|
overridevirtual |
Remove a collision shape from the body.
To remove a collision shape, you need to specify the pointer to the proxy shape that has been returned when you have added the collision shape to the body.
| proxyShape | The pointer of the proxy shape you want to remove |
Reimplemented from reactphysics3d::CollisionBody.
| void RigidBody::setAngularDamping | ( | decimal | angularDamping | ) |
Set the angular damping factor.
| angularDamping | The angular damping factor of this body |
| void RigidBody::setAngularVelocity | ( | const Vector3 & | angularVelocity | ) |
Set the angular velocity.
| angularVelocity | The angular velocity vector of the body |
| void RigidBody::setCenterOfMassLocal | ( | const Vector3 & | centerOfMassLocal | ) |
Set the local center of mass of the body (in local-space coordinates)
If you set the center of mass with the method, it will not be computed automatically using collision shapes.
| centerOfMassLocal | The center of mass of the body in local-space coordinates |
| void RigidBody::setInertiaTensorLocal | ( | const Matrix3x3 & | inertiaTensorLocal | ) |
Set the local inertia tensor of the body (in body coordinates)
If the inertia tensor is set with this method, it will not be computed using the collision shapes of the body.
| inertiaTensorLocal | The 3x3 inertia tensor matrix of the body in local-space coordinates |
| void RigidBody::setInverseInertiaTensorLocal | ( | const Matrix3x3 & | inverseInertiaTensorLocal | ) |
Set the inverse local inertia tensor of the body (in body coordinates)
If the inverse inertia tensor is set with this method, it will not be computed using the collision shapes of the body.
| inverseInertiaTensorLocal | The 3x3 inverse inertia tensor matrix of the body in local-space coordinates |
| void RigidBody::setLinearDamping | ( | decimal | linearDamping | ) |
Set the linear damping factor.
| linearDamping | The linear damping factor of this body |
| void RigidBody::setLinearVelocity | ( | const Vector3 & | linearVelocity | ) |
Set the linear velocity of the body.
| linearVelocity | Linear velocity vector of the body |
| void RigidBody::setMass | ( | decimal | mass | ) |
Set the mass of the rigid body.
| mass | The mass (in kilograms) of the body |
| void RigidBody::setMaterial | ( | const Material & | material | ) |
Set a new material for this rigid body.
| material | The material you want to set to the body |
|
overridevirtual |
Set the current position and orientation.
| transform | The transformation of the body that transforms the local-space of the body into world-space |
Reimplemented from reactphysics3d::CollisionBody.
| void RigidBody::setType | ( | BodyType | type | ) |
Set the type of the body (static, kinematic or dynamic)
The type of the body can either STATIC, KINEMATIC or DYNAMIC as described bellow: STATIC : A static body has infinite mass, zero velocity but the position can be changed manually.
A static body does not collide with other static or kinematic bodies. KINEMATIC : A kinematic body has infinite mass, the velocity can be changed manually and its position is computed by the physics engine. A kinematic body does not collide with other static or kinematic bodies. DYNAMIC : A dynamic body has non-zero mass, non-zero velocity determined by forces and its position is determined by the physics engine. A dynamic body can collide with other dynamic, static or kinematic bodies.
| type | The type of the body (STATIC, KINEMATIC, DYNAMIC) |
|
inlineprotected |
Update the world inverse inertia tensor of the body.
The inertia tensor I_w in world coordinates is computed with the local inverse inertia tensor I_b^-1 in body coordinates by I_w = R * I_b^-1 * R^T where R is the rotation matrix (and R^T its transpose) of the current orientation quaternion of the body.
|
protected |
Center of mass of the body in local-space coordinates.
The center of mass can therefore be different from the body origin


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Deploying a cluster is hard. Deploying a database cluster is harder. Deploying a database cluster repeatedly to the cloud is an unimaginable headache. Nowadays, IaC tools allows teams to automatically provision the complex intertwined cloud infrastructure in a deterministic manner. There can be multiple reasons why you would want to invest efforts into writing code for automating the deployment of a database cluster:
- Performance testing your applications' access patterns by pointing them to your database
- Documenting the custom configurations made while setting up the database
- Safely and quickly replicating environments for staging, testing, DR, etc
In this post, we'll look at deploying a MongoDB cluster to AWS with 1 primary (master) node and n secondary (data) nodes. We'll codify all our configurations with Terraform, shell scripts and Python scripts, to launch and bootstrap our cluster. This is the architecture diagram of the deployment:
Let's go over the resources that are going to be created:
- A VPC to isolate and contain all the instances
- 3 Public subnets and 3 Private subnets spread across 3 Availability Zones
- A Bastion Host (or Jump Box) for accessing the instances in the private subnets from an external network
- A NAT instance to provide internet access to the instances in the private subnets. (Side tip: NAT Gateway costs stack up a lot quickly than you can anticipate. Go for a NAT instance if your workloads aren't critical)
All the source code is available at this GitHub repository. The code is structured as different Terraform modules such as VPC, JumpBox, MongoDB Cluster, etc. You can visit the repository for installation prerequisites and instructions on how to run the project. Here's a snippet of the main.tf file which utilizes all the Terraform modules:
module "vpc" { source = "./vpc" key_name = "${module.key_pair.key_name}" vpc_name = "${var.vpc_name}" } module "key_pair" { source = "./key_pair" key_name = "mongo-key-pair" public_key = "${file("~/.ssh/id_rsa.pub")}" } module "jumpbox" { source = "./jumpbox" key_name = "${module.key_pair.key_name}" vpc_id = "${module.vpc.vpc_id}" subnet_id = "${module.vpc.public_subnet_ids[1]}" } module "mongodb_cluster" { source = "./mongodb_cluster" key_name = "${module.key_pair.key_name}" vpc_id = "${module.vpc.vpc_id}" vpc_cidr_block = "${module.vpc.vpc_cidr_block}" primary_node_type = "${var.primary_node_type}" secondary_node_type = "${var.secondary_node_type}" private_subnet_ids = "${module.vpc.private_subnet_ids}" jumpbox_public_ip = "${module.jumpbox.jumpbox_public_ip}" replica_set_name = "${var.replica_set_name}" num_secondary_nodes = "${var.num_secondary_nodes}" mongo_username = "${var.mongo_username}" mongo_database = "${var.mongo_database}" mongo_password = "${var.mongo_password}" }
The MongoDB cluster module takes in a lot of configurable parameters which can be supplied by the terraform.tfvars file:
vpc_name = "mongo_vpc" replica_set_name = "mongoRs" num_secondary_nodes = 3 mongo_username = "admin" mongo_password = "mongo4pass" mongo_database = "admin" primary_node_type = "t2.micro" secondary_node_type = "t2.micro"
The MongoDB Cluster Module
We're going to deploy MongoDB v4.0 using the Ubuntu 18.04 AMI. This page from the official MongoDB documentation delineates steps to follow for installing MongoDB on Ubuntu. Just browsing through the insane number of steps involved or the confusing order of steps, you can imagine the dividend of scripting the commands rather than scampering through the documentation to figure out what worked the last time. Additionally, since this isn't a single node deployment, we need to deploy a replica set for MongoDB. Here's excellent documentation which expands on the replication features of MongoDB. And here's the documentation specifying the steps needed to deploy a ReplicaSet
The main.tf file for the MongoDB cluster module contains the code for creating the resources like EC2 instances, IAM policies, Security Groups, etc. Using Terraform's file provisioner, certain scripts and files (like the private key file needed to be shared by all the participating nodes) are uploaded to the instances while creating them. But wait, how can Terraform upload a file from your laptop to an instance launched in an AWS private subnet? Check out the nifty "bastion_host" parameter in the connection block:
provisioner "file" { source = "${path.module}/keyFile" destination = "/home/ubuntu/keyFile" connection { type = "ssh" user = "ubuntu" host = "${self.private_ip}" agent = false private_key = "${file("~/.ssh/id_rsa")}" bastion_host = "${var.jumpbox_public_ip}" bastion_user = "ec2-user" } }
Here's a snippet for creating the Secondary nodes. The "count" parameter (passed by the user) controls how many nodes to create. The instance is placed in any of the 3 private subnets in a round-robin manner.
resource "aws_instance" "mongo_secondary" { count = "${var.num_secondary_nodes}" ami = "${data.aws_ami.ubuntu_18_image.id}" instance_type = "${var.secondary_node_type}" key_name = "${var.key_name}" subnet_id = "${var.private_subnet_ids[count.index % length(var.private_subnet_ids)]}" user_data = "${data.template_file.userdata.rendered}" vpc_security_group_ids = ["${aws_security_group.mongo_sg.id}"] iam_instance_profile = "${aws_iam_instance_profile.mongo-instance-profile.name}" root_block_device { volume_type = "standard" } tags = { Name = "Mongo-Secondary_${count.index + 1}" Type = "secondary" } }
The userdata shell script contains the bulk of the configuration. It scans the AWS environment for the cluster members and configures each instance with the private IPs of other members. This is accomplished by using the EC2 Instance Metadata Service. Also, each instance has a Tag attached to it which helps to identify whether it's a Primary or Secondary node. Here are a few commands from the userdata shell script which creates MongoDB configuration and service files:
sed -i 's/<IP_ADDRESS>/<IP_ADDRESS>/g' /etc/mongod.conf cat >> /etc/mongod.conf <<EOL security: keyFile: /opt/mongodb/keyFile replication: replSetName: ${replica_set_name} EOL chown ubuntu:ubuntu /etc/mongod.conf cat >> /etc/systemd/system/mongod.service <<EOL [Unit] Description=High-performance, schema-free document-oriented database After=network.target [Service] User=mongodb ExecStart=/usr/bin/mongod --quiet --config /etc/mongod.conf [Install] WantedBy=multi-user.target EOL
Go ahead and deploy the cluster in your AWS environment. Make sure you have a public-private keypair in the ~/.ssh directory. Use ssh-keygen to create the key files. Install Terraform and the AWS CLI. Create ~/.aws/credentials file to store your AWS Secret Key and Access Key locally for Terraform to use. I hope everything works great on the first try. If not, please feel free to reach out and I'll be more than happy to help!


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Nikola Tesla - The Futurist
Nikola Tesla was a Serbian-American inventor, electrical engineer, mechanical engineer, and futurist.
About Nikola Tesla
Nikola Tesla (/ˈtɛslə/ TESS-lə; Serbian Cyrillic: Никола Тесла,[2] pronounced [nǐkola têsla];[a] 10 July 1856 – 7 January 1943) was a Serbian-American[5][6][7] inventor, electrical engineer, mechanical engineer, and futurist best known for his contributions to the design of the modern alternating current (AC) electricity supply system.[8]
Born and raised in the Austrian Empire, Tesla studied engineering and physics in the 1870s without receiving a degree, gaining practical experience in the early 1880s working in telephony and at Continental Edison in the new electric power industry. In 1884 he emigrated to the United States, where he became a naturalized citizen. He worked for a short time at the Edison Machine Works in New York City before he struck out on his own. With the help of partners to finance and market his ideas, Tesla set up laboratories and companies in New York to develop a range of electrical and mechanical devices. His alternating current (AC) induction motor and related polyphase AC patents, licensed by Westinghouse Electric in 1888, earned him a considerable amount of money and became the cornerstone of the polyphase system which that company eventually marketed.
Scientific Contributions of Nikola Tesla
- AC Power (alternating current)
- Tesla Coil
- Magnifying Transmitter
- Tesla Turbine
- Shadowgraph
- Radio
- Neon Lamp
- Hydroelectric Power
- Induction Motor
- Radio Controlled Boat
Nikola Tesla Image Gallery
Plaques and memorials
- The Nikola Tesla Memorial Centre in Smiljan, Croatia, opened in 2006. It features a statue of Tesla designed by sculptor Mile Blažević.
- A plaque depicting a relief of Nikola Tesla is present on the Old City Hall in Zagreb, Croatia's capital, commemorating his proposal to build an alternating current power station, which he made to the city council.[300] The plaque quotes Tesla's statement, given in the building on 24 May 1892, which reads: "As a son of this country, I consider it my duty to help the City of Zagreb in every way, either through counsel or through action"
- On 7 July 2006, on the corner of Masarykova and Preradovićeva streets in the Lower Town area in Zagreb, a monument of Tesla was unveiled. This monument was designed by Ivan Meštrović in 1952 and was transferred from the Zagreb-based Ruđer Bošković Institute where it had spent previous decades
- A monument to Tesla was established at Niagara Falls, New York. This monument portraying Tesla reading a set of notes was sculpted by Frano Kršinić. It was presented to the United States by Yugoslavia in 1976 and is an identical copy of the monument standing in front of the University of Belgrade Faculty of Electrical Engineering.
- A monument of Tesla standing on a portion of an alternator was established at Queen Victoria Park in Niagara Falls, Ontario, Canada. The monument was officially unveiled on 9 July 2006 on the 150th anniversary of Tesla's birth. The monument was sponsored by St. George Serbian Church, Niagara Falls, and designed by Les Drysdale of Hamilton, Ontario.[304][305] Drysdale's design was the winning design from an international competition
- A monument of Tesla was unveiled in Baku in 2013. Presidents Ilham Aliyev and Tomislav Nikolić attended a ceremony of unveiling
- In 2012 Jane Alcorn, president of the nonprofit group Tesla Science Center at Wardenclyffe, and Matthew Inman, creator of web cartoon The Oatmeal, raised a total of $2,220,511 – $1,370,511 from a campaign and $850,000 from a New York State grant—to buy the property where Wardenclyffe Tower once stood and eventually turn it into a museum.[308][309] The group began negotiations to purchase the Long Island property from Agfa Corporation in October 2012.[310] The purchase was completed in May 2013.[311] The preservation effort and history of Wardenclyffe is the subject of a documentary by Tesla activist/filmmaker Joseph Sikorski called Tower to the People—Tesla's Dream at Wardenclyffe Continues
- A commemorative plaque honoring Nikola Tesla was installed on the façade of the New Yorker Hotel by the IEEE
- An intersection named after Tesla, Nikola Tesla Corner, is located at Sixth Avenue and 40th Street, outside Bryant Park in Manhattan, New York City. The placement of the sign was due to the efforts of the Croatian Club of New York in cooperation with New York City officials, and Dr. Ljubo Vujovic of the Tesla Memorial Society of New York.
- A bust and plaque honoring Tesla is outside the Serbian Orthodox Cathedral of Saint Sava (formerly known as Trinity Chapel) at 20 West 26th Street in New York City.


- If you see fire or smoke
- Help anyone who is in immediate danger, as long as there is no risk to your own
life.
- Leave the premises.
- Set off the fire alarm (stations are very close to emergency exits).
- Use the stairs to leave the building (never use the elevators).
- Close all doors behind you to make sure that the fire doesn’t spread.
- Dial 911 as soon as you are in a safe area.
- Do not go back inside for any reason.
If you hear a fire alarm go off
- Help anyone who is in immediate danger, as long as there is no risk to your own
life.
- Leave the premises.
- Use the stairs to leave the building (never use the elevators).
- Close all doors behind you to make sure that the fire doesn’t spread.
- Keep your distance from the premises (minimum of 100 metres) so that those who are following
behind you can exit easily, and to make firefighters’ jobs easier.
- Do not go back inside for any reason.
Meeting points
- The Dow Planetarium parking lot, at the corner of Peel and Notre Dame Streets, at the
northeastern corner of ÉTS.
- In the wintertime, people who are evacuated will be escorted, as soon as possible, to the
hall in Pavilion B and the common areas of the dormitories located at 301 Peel Street and
1045 Ottawa Street.
Returning to the building
- You can return to the building as soon as Security announces that it is safe to do so.
- This authorization will be announced over a megaphone at the meeting point.


For development of Phantasma applications it is recommended you run a Phantasma node locally. It acts as your own personal blockchain network. The following instructions explain how to do this on Windows. Other operating systems are also supported and instructions can be found in the following section of this document. You can later move to the official test network where multiple nodes are running, in order to test your dapp under a more realistic enviroment.
To get started download a pre-compiled build which comes bundled in the official SDK release: https://github.com/phantasma-io/PhantasmaSDK/releases/latest - the files you need reside under Tools\Spook in the .zip file
Note - you will need .NET runtime 3.1 installed on your desktop https://dotnet.microsoft.com/download
To bootstrap your own test net just run a single instance of Phantasma node using the following arguments:
spook-cli -node.wif=L2LGgkZAdupN2ee8Rs6hpkc65zaGcLbxhbSDGq8oh6umUxxzeW25 -nexus.name=simnet
#To enable the RPC server add this argument to the line above
-rpc.enabled=true
Otherwise you can compile the latest yourself from the source available in this repository.
To compile and publish the source code for you will need the following:
Pull or download the following GitHub Repositories
Ensure both of these sit in the same root directory on your PC and are in folders that match the above. For example:
Build and publish the code
The files needed to run a node will now be in PhantasmaSpook\Phantasma.CLI\Publish
As per above you can run it with the following command:
dotnet Spook.dll -node.wif=L2LGgkZAdupN2ee8Rs6hpkc65zaGcLbxhbSDGq8oh6umUxxzeW25 -nexus.name=simnet
#To enable the RPC server add this argument to the line above
-rpc.enabled=true
There are two different possibilities to configure Spook:
Every config paramater is usable in the configuration file and as a cli argument.
config.json
.Spook can be run in three different modes:
Note, you cannot have shell and tui enabled at the same time.


--- layout: archive title: Zulip Chat Archive permalink: /stream/113489-new-members/topic/universal.20properties.20for.20topology.html ---
Does mathlib already have lemmas for some universal properties? One in particular I'm interested in is for subspaces/subtypes. This is just the statement that if A is a subspace of X, and T any other space, then f : T -> A is continuous iff i o f is continuous where i is the inclusion of A into X, in this case just subtype.val.
I think it's already there
something about induced / coinduced topology
It's also embedding.continuous_iff
plus embedding_subtype_val
I don't see that exact theorem, but it's an easy corollary of tendsto_subtype_rng
or embedding_subtype_val
continuous_induced_rng
?
yes, but it needs restatement
also couldn't that theorem be an iff?
Ah yep, I think continuous_induced_rng works well enough
I only needed the forward direction, but it probably could be restated as an iff yeah
you simp
-minded people /s
Haven't I mentioned before that over-reliance on defeq is an anti-pattern that leads to non-modularity and code brittleness?
it's not just about simp
Also, out of curiosity what does rng/dom stand for?
range domain?
rng
is not a standard abbreviation, it should probably be renamed
also neither of the two rng
theorems mentions range
I guess it should be cod
instead (for codomain)
Last updated: Apr 24 2020 at 19:02 UTC


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--- layout: post title: "Maybe catamorphism" description: "The catamorphism for Maybe is just a simplification of its fold." date: 2019-05-20 6:04 UTC tags: [Software Design, Haskell] --- {% include JB/setup %}
{{ page.description }}
This article is part of an article series about catamorphisms. A catamorphism is a universal abstraction that describes how to digest a data structure into a potentially more compact value.
This article presents the catamorphism for Maybe, as well as how to identify it. The beginning of this article presents the catamorphism in C#, with examples. The rest of the article describes how to deduce the catamorphism. This part of the article presents my work in Haskell. Readers not comfortable with Haskell can just read the first part, and consider the rest of the article as an optional appendix.
Maybe is a data container that models the absence or presence of a value. Contrary to null, Maybe has a type, so offers a sane and reasonable way to model that situation.
This article uses Church-encoded Maybe. Other, alternative implementations of Maybe are possible. The catamorphism for Maybe is the Match
method:
TResult Match<TResult>(TResult nothing, Func<T, TResult> just);
Like the Peano catamorphism, the Maybe catamorphism is a pair of a value and a function. The nothing
value corresponds to the absence of data, whereas the just
function handles the presence of data.
Given, for example, a Maybe containing a number, you can use Match
to get the value out of the Maybe:
> IMaybe<int> maybe = new Just<int>(42); > maybe.Match(0, x => x) 42 > IMaybe<int> maybe = new Nothing<int>(); > maybe.Match(0, x => x) 0
The functionality is, however, more useful than a simple get-value-or-default operation. Often, you don't have a good default value for the type potentially wrapped in a Maybe object. In the core of your application architecture, it may not be clear how to deal with, say, the absence of a Reservation
object, whereas at the boundary of your system, it's evident how to convert both absence and presence of data into a unifying type, such as an HTTP response:
Maybe<Reservation> maybe = // ... return maybe .Select(r => Repository.Create(r)) .Match<IHttpActionResult>( nothing: Content( HttpStatusCode.InternalServerError, new HttpError("Couldn't accept.")), just: id => Ok(id));
This enables you to avoid special cases, such as null Reservation
objects, or magic numbers like -1
to indicate the absence of id
values. At the boundary of an HTTP-based application, you know that you must return an HTTP response. That's the unifying type, so you can return 200 OK
with a reservation ID in the response body when data is present, and 500 Internal Server Error
when data is absent.
As in the previous article, I'll use Fix
and cata
as explained in Bartosz Milewski's excellent article on F-Algebras.
While F-Algebras and fixed points are mostly used for recursive data structures, you can also define an F-Algebra for a non-recursive data structure. You already saw an example of that in the article about Boolean catamorphism. The difference between Boolean values and Maybe is that the just case of Maybe carries a value. You can model this as a Functor
with both a carrier type and a type argument for the data that Maybe may contain:
data MaybeF a c = NothingF | JustF a deriving (Show, Eq, Read) instance Functor (MaybeF a) where fmap _ NothingF = NothingF fmap _ (JustF x) = JustF x
I chose to call the 'data type' a
and the carrier type c
(for carrier). As was also the case with BoolF
, the Functor
instance ignores the map function because the carrier type is missing from both the NothingF
case and the JustF
case. Like the Functor
instance for BoolF
, it'd seem that nothing happens, but at the type level, this is still a translation from MaybeF a c
to MaybeF a c1
. Not much of a function, perhaps, but definitely an endofunctor.
In the previous articles, it was possible to work directly with the fixed points of both functors; i.e. Fix BoolF
and Fix NatF
. Haskell isn't happy about attempts to define various instances for Fix (MaybeF a)
, so in order to make this easier, you can define a newtype
wrapper:
newtype MaybeFix a = MaybeFix { unMaybeFix :: Fix (MaybeF a) } deriving (Show, Eq, Read)
In order to make it easier to work with MaybeFix
you can add helper functions to create values:
nothingF :: MaybeFix a nothingF = MaybeFix $ Fix NothingF justF :: a -> MaybeFix a justF = MaybeFix . Fix . JustF
You can now create MaybeFix
values to your heart's content:
Prelude Fix Maybe> justF 42 MaybeFix {unMaybeFix = Fix (JustF 42)} Prelude Fix Maybe> nothingF MaybeFix {unMaybeFix = Fix NothingF}
That's all you need to identify the catamorphism.
At this point, you have two out of three elements of an F-Algebra. You have an endofunctor (MaybeF
), and an object a
, but you still need to find a morphism MaybeF a c -> c
. Notice that the algebra you have to find is the function that reduces the functor to its carrier type c
, not the 'data type' a
. This takes some time to get used to, but that's how catamorphisms work. This doesn't mean, however, that you get to ignore a
, as you'll see.
As in the previous article, start by writing a function that will become the catamorphism, based on cata
:
maybeF = cata alg . unMaybeFix where alg NothingF = undefined alg (JustF x) = undefined
While this compiles, with its undefined
implementations, it obviously doesn't do anything useful. I find, however, that it helps me think. How can you return a value of the type c
from the NothingF
case? You could pass an argument to the maybeF
function:
maybeF n = cata alg . unMaybeFix where alg NothingF = n alg (JustF x) = undefined
The JustF
case, contrary to NothingF
, already contains a value, and it'd be incorrect to ignore it. On the other hand, x
is a value of type a
, and you need to return a value of type c
. You'll need a function to perform the conversion, so pass such a function as an argument to maybeF
as well:
maybeF :: c -> (a -> c) -> MaybeFix a -> c maybeF n f = cata alg . unMaybeFix where alg NothingF = n alg (JustF x) = f x
This works. Since cata
has the type Functor f => (f a -> a) -> Fix f -> a
, that means that alg
has the type f a -> a
. In the case of MaybeF
, the compiler infers that the alg
function has the type MaybeF a c -> c
, which is just what you need!
You can now see what the carrier type c
is for. It's the type that the algebra extracts, and thus the type that the catamorphism returns.
Notice that maybeF
, like the above C# Match
method, takes as arguments a pair of a value and a function (together with the Maybe value itself). Those are two representations of the same idea. Furthermore, this is nearly identical to the maybe
function in Haskell's Data.Maybe
module. I found if fitting, therefore, to name the function maybeF
.
You can implement most other useful functionality with maybeF
. Here's the Functor
instance:
instance Functor MaybeFix where fmap f = maybeF nothingF (justF . f)
Since fmap
should be a structure-preserving map, you'll have to map the nothing case to the nothing case, and just to just. When calling maybeF
, you must supply a value for the nothing case and a function to deal with the just case. The nothing case is easy to handle: just use nothingF
.
In the just case, first apply the function f
to map from a
to b
, and then use justF
to wrap the b
value in a new MaybeFix
container to get MaybeFix b
.
Applicative
is a little harder, but not much:
instance Applicative MaybeFix where pure = justF f <*> x = maybeF nothingF (<$> x) f
The pure
function is just justF (pun intended). The apply operator <*>
is more complex.
Both f
and x
surrounding <*>
are MaybeFix
values: f
is MaybeFix (a -> b)
, and x
is MaybeFix a
. While it's becoming increasingly clear that you can use a catamorphism like maybeF
to implement most other functionality, to which MaybeFix
value should you apply it? To f
or x
?
Both are possible, but the code looks (in my opinion) more readable if you apply it to f
. Again, when f
is nothing, return nothingF
. When f
is just, use the functor instance to map x
(using the infix fmap
alias <$>
).
The Monad
instance, on the other hand, is almost trivial:
instance Monad MaybeFix where x >>= f = maybeF nothingF f x
As usual, map nothing to nothing by supplying nothingF
. f
is already a function that returns a MaybeFix b
value, so just use that.
The Foldable
instance is likewise trivial (although, as you'll see below, you can make it even more trivial):
instance Foldable MaybeFix where foldMap = maybeF mempty
The foldMap
function must return a Monoid
instance, so for the nothing case, simply return the identity, mempty. Furthermore, foldMap
takes a function a -> m
, but since the foldMap
implementation is point-free, you can't 'see' that function as an argument.
Finally, for the sake of completeness, here's the Traversable
instance:
instance Traversable MaybeFix where sequenceA = maybeF (pure nothingF) (justF <$>)
In the nothing case, you can put nothingF
into the desired Applicative
with pure
. In the just case you can take advantage of the desired Applicative
being also a Functor
by simply mapping the inner value(s) with justF
.
Since the Applicative
instance for MaybeFix
equals pure
to justF
, you could alternatively write the Traversable
instance like this:
instance Traversable MaybeFix where sequenceA = maybeF (pure nothingF) (pure <$>)
I like this alternative less, since I find it confusing. The two appearances of pure
relate to two different types. The pure
in pure nothingF
has the type MaybeFix a -> f (MaybeFix a)
, while the pure
in pure <$>
has the type a -> MaybeFix a
!
Both implementations work the same, though:
Prelude Fix Maybe> sequenceA (justF ("foo", 42)) ("foo",MaybeFix {unMaybeFix = Fix (JustF 42)})
Here, I'm using the Applicative
instance of (,) String
.
Finally, you can implement conversions to and from the standard Maybe
type, using ana
as the dual of cata
:
toMaybe :: MaybeFix a -> Maybe a toMaybe = maybeF Nothing return fromMaybe :: Maybe a -> MaybeFix a fromMaybe = MaybeFix . ana coalg where coalg Nothing = NothingF coalg (Just x) = JustF x
This demonstrates that MaybeFix
is isomorphic to Maybe
, which again establishes that maybeF
and maybe
are equivalent.
As usual, the above maybeF
isn't the only possible catamorphism. A trivial variation is to flip its arguments, but other variations exist.
It's a recurring observation that a catamorphism is just a generalisation of a fold. In the above code, the Foldable
instance already looked as simple as anyone could desire, but another variation of a catamorphism for Maybe is this gratuitously embellished definition:
maybeF :: (a -> c -> c) -> c -> MaybeFix a -> c maybeF f n = cata alg . unMaybeFix where alg NothingF = n alg (JustF x) = f x n
This variation redundantly passes n
as an argument to f
, thereby changing the type of f
to a -> c -> c
. There's no particular motivation for doing this, apart from establishing that this catamorphism is exactly the same as the fold:
instance Foldable MaybeFix where foldr = maybeF
You can still implement the other instances as well, but the rest of the code suffers in clarity. Here's a few examples:
instance Functor MaybeFix where fmap f = maybeF (const . justF . f) nothingF instance Applicative MaybeFix where pure = justF f <*> x = maybeF (const . (<$> x)) nothingF f instance Monad MaybeFix where x >>= f = maybeF (const . f) nothingF x
I find that the need to compose with const
does nothing to improve the readability of the code, so this variation is mostly, I think, of academic interest. It does show, though, that the catamorphism of Maybe is isomorphic to its fold, as the diagram in the overview article indicated:
You can demonstrate that this variation, too, is isomorphic to Maybe
with a set of conversion:
toMaybe :: MaybeFix a -> Maybe a toMaybe = maybeF (const . return) Nothing fromMaybe :: Maybe a -> MaybeFix a fromMaybe = MaybeFix . ana coalg where coalg Nothing = NothingF coalg (Just x) = JustF x
Only toMaybe
has changed, compared to above; the fromMaybe
function remains the same. The only change to toMaybe
is that the arguments have been flipped, and return
is now composed with const
.
Since (according to Conceptual Mathematics) isomorphisms are transitive this means that the two variations of maybeF
are isomorphic. The latter, more complex, variation of maybeF
is identical foldr
, so we can consider the simpler, more frequently encountered variation a simplification of fold.
The catamorphism for Maybe is the same as its Church encoding: a pair made from a default value and a function. In Haskell's base library, this is simply called maybe
. In the above C# code, it's called Match
.
This function is total, and you can implement any other functionality you need with it. I therefore consider it the canonical representation of Maybe, which is also why it annoys me that most Maybe implementations come equipped with partial functions like fromJust
, or F#'s Option.get
. Those functions shouldn't be part of a sane and reasonable Maybe API. You shouldn't need them.
In this series of articles about catamorphisms, you've now seen the first example of catamorphism and fold coinciding. In the next article, you'll see another such example - probably the most well-known catamorphism example of them all.
Next: List catamorphism.


addClusters.Rd
This function will identify clusters from a reduced dimensions object in an ArchRProject or from a supplied reduced dimensions matrix.
addClusters(input = NULL, reducedDims = "IterativeLSI", name = "Clusters", sampleCells = NULL, seed = 1, method = "Seurat", dimsToUse = NULL, corCutOff = 0.75, knnAssign = 10, nOutlier = 20, verbose = TRUE, tstart = NULL, force = FALSE, ...)
| input | Either (i) an |
|---|---|
| reducedDims | The name of the |
| name | The column name of the cluster label column to be added to |
| sampleCells | UNCLEAR. FIX AND ADD LEAVE JJJ FOR ME TO CHECK. An integer specifying the number of cells to subsample and perform clustering on. The remaining cells will be assigned to the cluster of the nearest subsampled cell. |
| seed | A number to be used as the seed for random number generation required in cluster determination. It is recommended to keep track of the seed used so that you can reproduce results downstream. |
| method | A string indicating the clustering method to be used. Supported methods are "Seurat" and "Scran". |
| dimsToUse | A vector containing the dimensions from the |
| corCutOff | A numeric cutoff for the correlation of each dimension to the sequencing depth. If the dimension has a correlation to sequencing depth that is greater than the |
| knnAssign | The number of nearest neighbors to be used during clustering for assignment of outliers (clusters with less than nOutlier cells). |
| nOutlier | The minimum number of cells required for a group of cells to be called as a cluster. If a group of cells does not reach this threshold, then the cells will be considered outliers and assigned to nearby clusters. |
| verbose | A boolean value indicating whether to use verbose output during execution of this function. Can be set to FALSE for a cleaner output. |
| tstart | A timestamp to measure how long the clustering analysis has been running relative to a start time. Useful for keeping track of how long clustering when running things like IterativeLSI. |
| force | A boolean value that indicates whether or not to overwrite data in a given column when the value passed to |
| ... | Additional arguments to be provided to Seurat::FindClusters or scran::buildSNNGraph (for example, knn = 50, jaccard = TRUE) |


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Constructor
new EZMQSubscriber(ip, port, subCB, subTopicCB)
Parameters:
| Name | Type | Description |
|---|---|---|
ip |
string | IP address. |
port |
number | Port number. |
subCB |
Callback | Callback to be called whenever received any event. |
subTopicCB |
Callback | Callback to be called whenever received any event on topic. |
- Source:
Methods
getIp() → {string}
Get the IP address of the publisher.
- Source:
Returns:
IP address.
- Type
- string
getPort() → {number}
Get the port of the subscriber.
- Source:
Returns:
Port number.
- Type
- number
setClientKeys(clientPrivateKey, clientPublicKey) → {EZMQErrorCode}
Set the security keys of client/its own.
Note:
(1) Key should be 40-character string encoded in the Z85 encoding format
(2) This API should be called before start() API.
Note:
(1) Key should be 40-character string encoded in the Z85 encoding format
(2) This API should be called before start() API.
Parameters:
| Name | Type | Description |
|---|---|---|
clientPrivateKey |
string | Client private/secret key. |
clientPublicKey |
string | Client public key. |
- Source:
Throws:
Will throw an error, if security is not enabled while building.
Returns:
EZMQ_OK on success, otherwise appropriate error code.
- Type
- EZMQErrorCode
setServerPublicKey(serverPublicKey) → {EZMQErrorCode}
Set the server public key.
Note:
(1) Key should be 40-character string encoded in the Z85 encoding format
(2) This API should be called before start() API. (3) If using the following API in secured mode:
subscribeWithIPPort then, setServerPublicKey API needs to be called before that.
Note:
(1) Key should be 40-character string encoded in the Z85 encoding format
(2) This API should be called before start() API. (3) If using the following API in secured mode:
subscribeWithIPPort then, setServerPublicKey API needs to be called before that.
Parameters:
| Name | Type | Description |
|---|---|---|
serverPublicKey |
string | Server public key. |
- Source:
Throws:
Will throw an error, if security is not enabled while building.
Returns:
EZMQ_OK on success, otherwise appropriate error code.
- Type
- EZMQErrorCode
start() → {EZMQErrorCode}
Starts SUB instance.
- Source:
Returns:
EZMQ_OK on success, otherwise appropriate error code.
- Type
- EZMQErrorCode
stop() → {EZMQErrorCode}
Stops SUB instance.
- Source:
Returns:
EZMQ_OK on success, otherwise appropriate error code.
- Type
- EZMQErrorCode
subscribe(topic) → {EZMQErrorCode}
Subscribe for event/messages. This API can be called to subscribe for all events or
subscribe events for given topic/s.
Note:
(1) If API is called without topic, it will subscribe for all the events.
(2) Topic can be a single topic [String] or list of topic [String list].
(3) Topic name should be as path format. For example: home/livingroom/
(4) Topic name can have letters [a-z, A-z], numerics [0-9] and special characters _ - . and /
Note:
(1) If API is called without topic, it will subscribe for all the events.
(2) Topic can be a single topic [String] or list of topic [String list].
(3) Topic name should be as path format. For example: home/livingroom/
(4) Topic name can have letters [a-z, A-z], numerics [0-9] and special characters _ - . and /
Parameters:
| Name | Type | Description |
|---|---|---|
topic |
string/stringlist | Subscribe for given topic. It can be empty. |
- Source:
Returns:
EZMQ_OK on success, otherwise appropriate error code.
- Type
- EZMQErrorCode
subscribeWithIPPort(ip, port, topic) → {EZMQErrorCode}
Subscribe for event/messages from given IP:Port on the given topic.
Note:
(1) It will be using same Subscriber socket for connecting to given ip:port.
(2) To unsubcribe use un-subscribe API with the same topic.
(3) Topic name should be as path format. For example: home/livingroom/
(4) Topic name can have letters [a-z, A-z], numerics [0-9] and special characters _ - . and /
(5) Topic will be appended with forward slash [/] in case, if application has not appended it
(6) If using in secured mode: Call setServerPublicKey(serverPublicKey) API with target server public key before calling this API.
Note:
(1) It will be using same Subscriber socket for connecting to given ip:port.
(2) To unsubcribe use un-subscribe API with the same topic.
(3) Topic name should be as path format. For example: home/livingroom/
(4) Topic name can have letters [a-z, A-z], numerics [0-9] and special characters _ - . and /
(5) Topic will be appended with forward slash [/] in case, if application has not appended it
(6) If using in secured mode: Call setServerPublicKey(serverPublicKey) API with target server public key before calling this API.
Parameters:
| Name | Type | Description |
|---|---|---|
ip |
string | Target[Publisher] IP address. |
port |
number | Target[Publisher] Port number. |
topic |
string | Topic to be subscribed. |
- Source:
Returns:
EZMQ_OK on success, otherwise appropriate error code.
- Type
- EZMQErrorCode
unSubscribe(topic) → {EZMQErrorCode}
Un-Subscribe for event/messages. This API can be called to unSubscribe for all events or
unSubscribe events for given topic/s.
Note:
(1) If API is called without topic, it will unsubscribe for all the events.
(2) Topic can be a single topic [String] or list of topic [String list].
(3) Topic name should be as path format. For example: home/livingroom/
(4) Topic name can have letters [a-z, A-z], numerics [0-9] and special characters _ - . and /
Note:
(1) If API is called without topic, it will unsubscribe for all the events.
(2) Topic can be a single topic [String] or list of topic [String list].
(3) Topic name should be as path format. For example: home/livingroom/
(4) Topic name can have letters [a-z, A-z], numerics [0-9] and special characters _ - . and /
Parameters:
| Name | Type | Description |
|---|---|---|
topic |
string/stringlist | UnSubscribe for given topic. It can be empty. |
- Source:
Returns:
EZMQ_OK on success, otherwise appropriate error code.
- Type
- EZMQErrorCode


Notebooks
Story: A discussion on the respective understanding and foolishnesses of various animals and some of their doings
A discussion on the respective understanding and foolishnesses of various animals and some of their doings
Title
A discussion on the respective understanding and foolishnesses of various animals and some of their doings
Collection
Summary
Some animals have' thoughts' (or 'understanding') and can talk as people do. According to ||kabbo (see p.891v), some animals stand upright like a man does. (Much of this story has not been translated.) ... a discourse upon the degrees of understanding possessed by various animals (L II.-8. 882-892).
Comments
1) Date on p.890: 21 November, 2) This story is found in Book II-8
Contributors
Date
November 1871
Categories
Keywords
understanding (of animals) , understanding (degrees of possessed by different animals) , understanding (thinking) , understanding ('thoughts') , understanding (and foolishness) , understanding (and speech) , understanding (of animals that have 'thoughts') , animals (the doings of) , animals (the understanding and foolishness of) , animals (that can talk) , animals (that stand upright like men) , animals (that have 'thoughts') , speech (and animals that have 'thoughts') , speech (animals that can talk)
Story Pages
882-892


How to Contribute¶
There are a few fairly easy ways for newcomers to substantially improve ForwardDiff, and
they all revolve around writing functions for Dual
numbers. This section
provides brief tutorials on how to make these contributions.
If you’re new GitHub, here’s an outline of the workflow you should use:
- Fork ForwardDiff
- Make a new branch on your fork, named after whatever changes you’ll be making
- Apply your code changes to the branch on your fork
- When you’re done, submit a PR to ForwardDiff to merge your fork into ForwardDiff’s master branch.
Manually Optimizing Unary Functions¶
To see a list of functions to pick from, look at ForwardDiff.AUTO_DEFINED_UNARY_FUNCS
:
julia> import ForwardDiff
julia> ForwardDiff.AUTO_DEFINED_UNARY_FUNCS
57-element Array{Symbol,1}:
:sqrt
:cbrt
:abs2
:inv
:log
:log10
:log2
:log1p
:exp
:exp2
:expm1
:sin
:cos
:tan
⋮
Some of these functions may have already been manually optimized. To see what functions have
already been done, go to src/dual.jl
, scroll down to the Special Cases
section, and
look at the functions under Manually Optimized
(further optimizations to these functions
are always welcome, if you can come up with something clever).
The functions in ForwardDiff.AUTO_DEFINED_UNARY_FUNCS
are automatically tested as part
of ForwardDiff’s test suite, so you don’t need to write tests yourself. You can test your
changes by running Pkg.test("ForwardDiff")
.
If everything passes, you can submit a PR to the ForwardDiff repository to share your work!
Implementing New Functions¶
Unary Functions Via Calculus.jl¶
The easiest way to add support for a new function is actually to define a derivative rule
for the function in Calculus’s symbolic differentiation code, which ForwardDiff then uses
to generate the function’s definition on Dual
numbers. To accomplish this:
- Open an issue in ForwardDiff with the title “Supporting f(x)” (obviously replacing “f(x)”” with the function you wish to support).
- Open a PR to Calculus that adds the relevant differentiation rule(s) and tests. In the PR’s description, be sure to mention the relevant ForwardDiff issue such that GitHub links the two.
- Once the PR to Calculus is accepted, we can check to make sure that the function works appropriately in ForwardDiff. If it does, then you’re done, and the issue in ForwardDiff can be considered resolved!
Manually Adding Functions to ForwardDiff¶
Some functions aren’t suitable for auto-definition via the Calculus package. An example of
such a function is the non-unary function atan2
, which is defined manually in
ForwardDiff/src/dual.jl
.
The process for manually adding functions to ForwardDiff without going through Calculus.jl
is essentially the same as the process for manually optimizing existing functions, with the
additional requirement that you’ll have to write the tests yourself. New tests for Dual
numbers can be placed in DualTest.jl.


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Having overseas customers, or importing or exporting goods internationally, doesn’t mean your business is operating overseas.
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A trustee can be a company or a person.
Self-managed super funds are a way of saving for your retirement. Most people contribute to a super fund that’s already been set up.
If you set up a self-managed super fund, you’re in charge. This means you decide where the fund invests its money and you are responsible for meeting super and tax laws.