デュアルクォータニオン スキニング チュートリアル・解説 C++ コード

Bar twist lbs bar twist dqs

Japanese version・日本語版。(英語・English version over here)

Anki: add syntax highlighting with javascript (highlight.js)

Tested on Anki 2.1.44 desktop version, however, I could not make it work for Ankidroid.

Find a tetrahedron circumcenter

Parking space in Tokyo / Japan

A guide to find and know what to expect when looking for parking areas in Tokyo Japan.

Mistakes to avoid when buying a car in Tokyo / Japan

A guide on what to expect when buying a car in Tokyo / Japan and pitfalls to avoid.

COM and DirectX

Getting started with DirectX 11

(mainly gathering resources for learning)

Curvature of a Distance field / Implicit surface

Draft notes

Curvature of a parametric curve

(Draft / notes)

[Maya C++] add control curve/spline attribute

Allow user to customize a 2D curve (spline etc.) to control some parameters such as color, grading and more.

Cyclic Coordonate descent Inverse Kynematic (CCD IK)

Blank SPI personality test - SPI性格検査・SPI模擬テスト・SPI問題集

Sample questions for the SPI personality test which is very popular in Job interviews (questions related to logic, language etc. are not present)

Efficient Maya development environment

How to setup your IDE so that clicking 'build' allows you to test and run your Maya plugin without extra steps or application restart.

Avoid SVD when looking for optimal rotation between point sets.

Draft note

Definition: Laplacian Matrix for triangle meshes

Definition of the Laplacian matrix and Laplace operator on a triangular mesh. I give an in depth explanation here.

[Maya C++ API] paint weights with MPxDeformer

Distributing Maya plugins

I will discuss various ways you can ship a Maya plugin to users.

Polar decomposition of a 3x3 matrix

Leaving [  C++ code ] to decompose a 3x3 matrix into rotation and scale/shear with polar decomposition.

Diffusing / smoothing weight map over a triangular mesh.

Showcasing simple procedures with C++ code to smooth / diffuse per vertex weights over a triangle mesh.


Normal to an implicit surface

Implicit surface a.k.a (signed) distance field: definition

Render by Elmar Glaubauf (artstation.com)

If I say "implicit surface" you may think of metaballs and marching cube, I'll show you there is more to it!

Phong illumination model (cheat sheet)

$$ f(  \vec p ) = \underbrace{I_a K_a}_{\color{red} \text{ambient component}} + \underbrace{\sum_i^\text{nb_lights} (\vec n( \vec p ) . \vec l_i) K_d I_i}_{\color{green} \text{diffuse component}} + \underbrace{\sum_i^\text{nb_lights} f_{spec}(\vec l_i( \vec p ), \vec v(\vec p)) K_s I_i}_{\color{blue} \text{specular component}} $$

I summarize the Phong illumination model with the above equation and explain all the terms one by one.

Anki tip, inserting furigana (pop up on mouse hover)

Here is how you can make furigana appear above kanjis in your anki flash cards like this: おはし上手じょうずですね!

Learning japanese: a life's journey

Learning a language is quite a challenge, here I will gather some resources and thoughts about learning Japanese.

MAYA_SHELF_PATH not working, empty Maya shelves

[Maya C++ API] Get selected vertices of a mesh

[Maya C++ API] Set skinning weight attributes

Some C++ Maya API code to set skin weights (multi attributes) of a skin cluster node.

Dual Quaternion Skinning with scale

DQS with scale applied on the second to last joint. Left, globally propagates until the last bone, right, scale localized to each joint.

Skeletal animation, forward kinematic

Maya MEL commands and procedures

Transforming implicit surface (distance field) and their gradient

[Maya C++ API] Save MPxData attribute on file

[Maya C++ API] Unable to unload plugin in Maya

Bulge free Dual Quaternion Skinning (Trick)

Left: standard DQS. Right DQS bulge correction (both use same automatic skin weight: "smooth bind" inside Maya).

[Maya C++ API] Per vertex color update in MPxDeformerNode

Code snippet in C++ to be able to update the color of a mesh with Maya API on a per vertex basis.

MAYA MEL wait for idle events/evalDeferred to finish

A trick to pause the script until evalDeferred / scriptJob / idle are executed.

Laplacian smoothing (C++ code to smooth a mesh)

Dropping a procedure to compute the Laplacian smoothing of a 3D mesh (with cotangent weights).

C++ code for cotangent weights over a triangular mesh

$$w_{ij} = \cot(\alpha_{ij}) + \cot(\beta_{ij})$$

Transform normals given a deformation map

Blender 2.5 - 2.7 tutorial to animate a cylinder

Maya summary

Summary of elementary Maya feature.

Gradient rules

Cheat sheet to differentiate expressions with the \( \nabla \) operator to compute gradients of various functions.

Design of a simple sphere deformer to displace a mesh model

Elastic Implicit Skinning: a Robust Iso-Surface Tracking for Interactive Character Skinning

Publication: ACM SIGGRAPH ASIA, 2014

Rodolphe Vaillant1,2, Gaël Guennebaud3, Loïc Barthe1Brian Wyvill2, Marie-Paule Cani4 

1IRIT - Université de Toulouse, 2University of Victoria, 3Inria Bordeaux,
4LJK - Grenoble Universités - Inria

Comparison of Implicit Skinning with our new Elastic Implicit Skinning. From right to left: Jeff in T-pose, Jeff rigged with implicit skinning, Jeff rigged with elastic implicit skinning, female model with implicit skinning then elastic implicit skinning.

With elastic implicit skinning the skin stretches automatically (without skinning weights) and the vertices distribution is more pleasing (notice the belly button stretch). Our approach is more robust, for instance the angle's range of joints is larger than implicit skinning (notice the triangle inversion of implicit skinning at the knee joint)

2D biharmonic stencil a.k.a bilaplacian operator

Draft / work in progress

Voro++.0.4.5 with cmake for easy compilation under windows

Dropping my code of the [ cmake version of voro++0.4.5 ]. It helped me to compile the voro++ library under windows with cmake.

Harmonic function: definitions and properties

This is the second part of my tutorial series on bounded harmonic functions. For a quick introduction and examples of use of harmonic functions read the first part. In this part I define harmonic functions and their properties. This is the hard part with a lot of mathematics. But it's a mandatory step to understand how harmonic functions work. This will allow you to apply them in a broader context and understand many scientific papers relying on these. In addition this will be my entry point to introduce Finite Element Method in future posts. So hang on it's worth it!

AnkiDroid: How to solve "Syncing error, type: 409, message: Conflict" problem

I ran into the infamous message "Syncing error, type: 409, message: Conflict" while syncing my AnkiDroid with AnkiWeb on my Nexus 4. Here is the solution:

Contour lines

3d graph


To represent a 2D function \( z = f(x,y) \) one can draw a 3D surface. The higher the \(z\) value the higher the point on the surface (see above).

How to generate bounded harmonic weights on a regular grid





Generating an height-map  is a good example to demonstrate how useful harmonic functions can be. In (a) user can stroke lines corresponding to different heights. In (b) we associate a height where the strokes lies. In (c) we compute the rest of the values automatically (black is zero, white is one). (d) is a 3D view of the heightmap in (c). It is a 2D function \( f: \mathbb R^2 \rightarrow \mathbb R\) which returns the height. The tutorial explains how to compute the unknown heights and ensure \(f\) is an harmonic function.


In this tutorial I give the basics to be able to compute harmonic functions \( f: \mathbb R^n \rightarrow \mathbb R\) over a regular grid/texture (in 1D, 2D or 3D). All you need is to set a few values on the grid that define a closed region (see figure above), then the remaining values are automatically computed using the so-called Laplace operator and solving a linear system of equations. After a quick and "mathless" presentation of an easy way to implement this in C++, I will explain the mathematical jargon. This tutorial is the first of series which will lead to more complicated techniques like Finite Element Methods (FEM).


Singular value decomposition of a 2x2 matrix (C++ code)

Dropping some [ code here] to do a singular value decomposition (SVD) of a 2 by 2 real matrix.

Source code for poisson disk sampling of a triangle mesh

2d poisson disk

Here you can download the C++ code] to do a Poisson disk sampling of a triangular mesh. The code is a simple wrapper for the vcglib library. It takes in input a std::vector of triangles and vertex position/normals and outputs std::vector of samples positions/normals computed with the Poisson disk sampling.

EDIT: Victor Martins pointed out that the above code doesn't compile on MAC and kindly provided an [  update] bundled with a newer version of vcglib.

N.B: if you are looking for a way to do Poisson disk sampling fast/in real-time take a look at this siggraph paper and matlab code. There is also a C++ implementation here.

3D viewer for Hermite Radial Basis Function

This is a simple demonstrator of the HRBF technique presented and explained here. You can visualize and edit the implicit surface generated with HRBF.

Curvature of a triangle mesh, definition and computation.

Defining and giving the formula to compute the curvature over a triangle mesh at some vertices.

C++ code for spline curves

2d spline

Dropping on github C++ code to compute spline curves of arbitrary dimensions 3D curves or 2D splines anything is possible. The class can be instantiated with any point type (1d (float), 2d, 3d etc.) as long as the appropriate operator overload are implemented. This class use the efficient blossom algorithm to compute a position on the curve.

Implicit Skinning: Real-Time Skin Deformation with Contact Modeling

Publication: ACM SIGGRAPH, 2013

Rodolphe Vaillant1,2, Loïc Barthe1, Gaël Guennebaud3, Marie-Paule Cani4, Damien Rhomer5, Brian Wyvill2, Olivier Gourmel1 and Mathias Paulin1

1IRIT - Université de Toulouse, 2University of Victoria, 3Inria Bordeaux,
4LJK - Grenoble Universités - Inria, 5CPE Lyon - Inria



  (a) (b)
  (c) (d)
(a) Self-intersection of the Armadillo's knee with dual quaternions skinning. (b) Implicit Skinning produces the skin fold and contact. (c), (d) two poses of the finger with Implicit Skinning generating the contact surface and organic bugle. (e) Implicit Skinning of an animated character around 95fps.

Dual Quaternions skinning tutorial and C++ codes

Bar twist lbs bar twist dqs

日本語版・Japanese version

In this entry I provide [  C++ codes ] to deform a mesh with the famous Dual Quaternion Skinning (DQS) deformer.

Convert implicit surface defined with global support to compact support

In mathematics functions are sometime characterized as compactly or globally supported. I will explain what it means and how to convert a function from global to compact support in the context of implicit surface modeling (i.e. boolean modeling with implicit surfaces as objects).

Trackball C++ code without quaternions

I'm leaving some code to handle a simple trackball interface to move 3D objects around. Trackballs give an intuitive rotation given an input mouse motion: given a clicked point and a second point moving on the screen we compute a rotation (that you apply to some 3D object in the scene) that gives the user the impression of dragging a 3D ball where we first clicked on it.

The code actually wasn't done by me, but I can't remember where I took it! Originally it was C code which I've wrapped up in a C++ class with way more comments and an example of how to use it. [  C++ trackball code ].

Compute Harmonic weights on a triangular mesh

Here I describe the discreet Laplace-Beltrami operator for a triangle mesh and how to derive the Laplacian matrix for that mesh. Then I provide [  C++ code ] to compute harmonic weights over a triangular mesh by solving the Laplace equation.

Building a new culture of teaching and learning

Theories around alternative systems for teaching and learning has always interested me, so I decided to open an entry about that.  My first contribution will be the English transcript of an inspiring video about education. I might put more articles/videos on this topic later.

Recipe for implicit surface reconstruction with HRBF

In this entry I'll explain and give code for the easiest method I know to reconstruct a surface represented by a scalar field \(f: \mathbb R^3 \rightarrow \mathbb R\) by interpolating a set of point with their normals. The method is called Hermite Radial Basis Function (HRBF) interpolation. The audience aimed is anyone with some basic knowledge about implicit surfaces (which people often know as metaballs and render with the marching cube algorithm)

Quick links:

C++ code to emulate openGL old direct mode drawing

glVertex3f(1.0f, 0.0f, 0.0f);
glVertex3f(0.0f, 1.0f, 0.0f);
glVertex3f(0.0f, 0.0f, 1.0f);

 [  compact version ] | [  modular version ]

Remember the old days when you were able to simply draw a few primitives with GL_POINTS, GL_LINES or GL_QUADS within a pair of good old begin() end(). Well I'm providing a C++ class which will enable you to do this again under OpenGL 3.1 or higher.

C code for 4x4 matrix inversion

Just leaving some code here to invert either column or row major 4x4 matrices.

Upgrade to CUDA 5.0: cudaMemcpyToSymbol invalid device symbol error

You have just upgraded to CUDA 5.0 and the function cudaMemcpyToSymbol() throws you the infamous "invalid device symbol" error. Here is what to do.

CUDA constant memory, namespace, and weird bugs

Edit: the usage of cudaMemcpyToSymbol describded below is deprecated since CUDA 4.1 (See also my new entry Upgrade to CUDA 5.0: cudaMemcpyToSymbol invalid device symbol error)

Today I want to discuss some issues I had with CUDA constant memory and share some workarounds.

Drag and drop not working in QTDesigner or QTCreator designer

This has upset me for some time and I finally found a forum entry solving this problem.

The problem: I wasn't able to drag&drop in QTDesigner any widgets from the widgets list to the form I was editing.
Solution found here: qtforum.org

You only need to add this entry to your /etc/X11/xorg.conf:

Section "Module"
Load "extmod"

Broken F4 shortcut in Qtcreator for cuda files ".cu"

Well I'm using QtCreator to code my CUDA project and there has been a lot of things bothering me. Among them is this F4 shortcut which doesn't work. The shortcut enables switching between the header and source file but apparently the extension .cu is not recognized as a C++ source file. Here is how to fix it.

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