Yamyam: 1版をインポートしました

2018-06-28T20:49:22Z

1版をインポートしました

2012年5月28日 (月) 15:48にwiki>Apinzonfによる

2012-05-28T15:48:21Z

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= Design =

Project: Mesh smoothing based on curvature flow operator in a diffusion equation.

Language: C, C++.

== Introduction ==

This document describe the methodology to achieve integration the mesh smoothing tool new in Blender.

This new tool go into the specials menu, because the tool do not working in real time.

{{RefBox
|mode=Edit Mode (Mesh)
|hotkey={{shortcut|W}}
|menu=Specials → Laplacian Smooth
|lang=en
}}

== Methodology ==

The project would divide into following parts:

=== Understanding the Blender source code ===

To Identify the key points for the project with base on Blender documentation, and other related documents.

* Operators [[Dev:2.5/Source/Architecture/Operators]]
* Laplacian implementation <tt>source/blender/editors/armature/meshlaplacian.c</tt>

=== Initialize data and necessary structures ===

The structures and functions necessary to implement this new tool, modified as follows the source code of my branch.

*<tt>soc-2012-sushi/source/blender/editors/mesh/mesh_intern.h</tt> <source lang="c">void MESH_OT_vertices_smooth_laplacian(struct wmOperatorType *ot);</source>
*<tt>soc-2012-sushi/source/blender/bmesh/intern/bmesh_operators_private.h</tt> <source lang="c">void bmo_vertexsmoothlaplacian_exec(BMesh *bm, BMOperator *op);</source>
*<tt>soc-2012-sushi/source/blender/editors/mesh/mesh_ops.c</tt> <source lang="c">WM_operatortype_append(MESH_OT_vertices_smooth_laplacian);</source>
*<tt>soc-2012-sushi/source/blender/bmesh/intern/bmesh_opdefines.c</tt> <source lang="c">static BMOpDefine bmo_vertexsmoothlaplacian_def = { ...</source>
*New file <tt>soc-2012-sushi/source/blender/bmesh/operators/bmo_smooth_laplacian.c</tt> <source lang="c">void bmo_vertexsmoothlaplacian_exec(BMesh *bm, BMOperator *op){...</source>
*<tt>soc-2012-sushi/source/blender/editors/mesh/editmesh_tools.c</tt> <source lang="c">void MESH_OT_vertices_smooth_laplacian(wmOperatorType *ot){...</source>
*<tt>soc-2012-sushi/source/blender/editors/mesh/editmesh_tools.c</tt> <source lang="c">static int edbm_do_smooth_laplacian_vertex_exec(bContext *C, wmOperator *op)...
</source>

=== Implement methods for the initial configuration ===

To achieve this goal it is necessary to implement the following methods in <tt>bmo_smooth_laplacian.c</tt> file.

* To initialize vertex index, parameters, and calculate initial ring area for each vertex. <source lang="c">void init_index();</source>
* To compute rings in structure for get neighbors to each vertex. <source lang="c">void compute_rings();</source>

=== Compute the Laplacian Matrix ===

To achieve this goal i must create a method to calculate the Laplacian of a vertex based on the technique proposed in the article by [http://multires.caltech.edu/pubs/ImplicitFairing.pdf Desbrun, et al].

<math>
L_{ij}=\left\{
\begin{array}{c}
w_{ij}=\cot \alpha _{ij}+\cot \beta _{ij} \\
\sum_{(i,j)\in E}^{k}-w_{ij} \\
0
\end{array}
\begin{array}{c}
if~(i,j)\in E \\
if~i=j \\
otherwise
\end{array}
\right\}
</math>

Where L is the laplacian matrix, w is the weigth between the vertex i and vertex j, and α and β are the opposite angles to edge between vertex i, and vertex j.

<source lang="c">float compute_weight(int vertex_i_id, int * neighbors_to_i);</source>

=== Integrate or use numerical library ===

Within the libraries present in Blender, I found that I can work with OpenNL, to solve the system of equations, besides that I have <tt>meshlaplacian.c</tt> guide document in which they solve a system similar to that I have.

=== Define the sparse linear system ===

I need to solve the following system of equations.

Difusion equation for mesh smoothing:

<math>\frac{\partial V}{\partial t}=\lambda L\left( V\right) </math>

Integrating the diffusion equation with a explicit Euler scheme:

<math>\left( I+\lambda dtL\right) V^{t+1}=V^{t}</math>

Where <math>V^{t}</math> is the actual position of vertex, and <math>V^{t+1}</math> is the vertex
after smoothing.

Solving the sparse linear system

<math>Ax=b</math>

Where:

<math>A=\left( I+\lambda dtL\right) </math>

<math>x=V^{t+1}</math>

<math>b=V^{t}</math>

=== Define and implement graphical user integration ===

=== Testing the tool ===

=== Generation of the documentation and tutorials ===

== Appendix ==

=== How would look the mesh smoothing tool in Blender ===

[[Image:Apinzonf_GSOC_2012_Diagram1.png|thumb|630px|Mesh Smoothng: a) Original Mesh. b) Smooth with Blender c) New mesh smooth method]]

In the figure above, you can see the problem applying smoothing with blender (Figure b), it shows how you lose detail at the edge on the eyelid of the eye. Figure c smoothing was performed with the method proposed and the detail was not lost on the eyelid.

=== Description of my development computer ===

* OS: Windows 7
* Builder System CMake 2.8.8, MS VS2010
* SVN tools: TortoiseSVN 1.7

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Yamyam: 1版 をインポートしました

2012年5月28日 (月) 15:48にwiki>Apinzonfによる

Yamyam: 1版をインポートしました