shape modeling

Shape ModelingShape ModelingVladimir Savchenko

[email protected]

Course DetailsCourse Details Course materials can be downloaded fromCourse materials can be downloaded fromhttp://cis.k.hosei.ac.jp/~vsavchen/SML/http://cis.k.hosei.ac.jp/~vsavchen/SML/ Evaluation:Evaluation: Attendance - 20Attendance - 20 Projects - 50Projects - 50 Exam - 30Exam - 30 Almost all lectures have exercises. Do Almost all lectures have exercises. Do

them! them! Some of them will be used during exams!!!Some of them will be used during exams!!!

PrefacePreface

What is CAGD and CG ?What is CAGD and CG ? An attempt to abstract from the complexity of An attempt to abstract from the complexity of

phenomenaphenomena

ExamplesExamples Global reconstruction from point setsGlobal reconstruction from point sets ( Head and Shell ( Head and Shell

reconstruction)reconstruction)

Examples - Surface Retouching Examples - Surface Retouching (Cont.)(Cont.)

Surface retouching of Surface retouching of a real polygonal a real polygonal modelmodel

• Left image. A “Stoned” model (courtesy of R. Scopigno and M. Left image. A “Stoned” model (courtesy of R. Scopigno and M. Calliery of Institute CNUCE). Model size – 88478 points. Calliery of Institute CNUCE). Model size – 88478 points.

• Right after surface retouching. Right after surface retouching.

Examples - Surface Retouching Examples - Surface Retouching (Cont.)(Cont.)

Examples- Examples- Surface Smoothing Surface Smoothing with CSRBFs (Cont.)with CSRBFs (Cont.)

Comparison of CSRBF smoothing and Laplacian smoothing.Comparison of CSRBF smoothing and Laplacian smoothing.

(a) (b)(a) (b)• (a) Original noisy sphere “Epcot” model, (770 vertices, 1536 polygons); (b) Smoothed (a) Original noisy sphere “Epcot” model, (770 vertices, 1536 polygons); (b) Smoothed

model after 5 iterations based on 11-point interpolation. Processing time: 0.6 s.model after 5 iterations based on 11-point interpolation. Processing time: 0.6 s.

200 iterations, 0.1 s. 1000 iterations, 0.41 s. 200 iterations, 0.1 s. 1000 iterations, 0.41 s. • Noisy sphere “Epcot” model after processing with Laplacian smoothing Noisy sphere “Epcot” model after processing with Laplacian smoothing


(a) (a) The original “Stanford Bunny” model (35947 vertices)The original “Stanford Bunny” model (35947 vertices)(b) Smoothed model after one iteration based on 11 points interpolation (b) Smoothed model after one iteration based on 11 points interpolation

(processing time 4.7 sec)(processing time 4.7 sec)(c) Smoothed model after one iteration based on 5 points interpolation(c) Smoothed model after one iteration based on 5 points interpolation(d) Smoothed model after 5 iterations based on 5 points interpolation (d) Smoothed model after 5 iterations based on 5 points interpolation

(a)

(b)

(c)

(d)


(a) The original “ballJoint” model (Cyberware Inc, (a) The original “ballJoint” model (Cyberware Inc, 34267 vertices)34267 vertices)

(b) Smoothed model after one iteration based on 11 (b) Smoothed model after one iteration based on 11 points interpolation (processing time 4.1 sec)points interpolation (processing time 4.1 sec)

Examples - Surface Simplification Examples - Surface Simplification with RBFs (Cont.)with RBFs (Cont.)

Visual results for the Horse model Visual results for the Horse model (a) - 96966 polygons (b) - 50% (c) - 30% (d) - 10% (e) - 3%(a) - 96966 polygons (b) - 50% (c) - 30% (d) - 10% (e) - 3%

Examples - Surface Simplification Examples - Surface Simplification with RBFs (Cont.)with RBFs (Cont.)

(a)(a) The modified “Stanford Bunny” model, simplified The modified “Stanford Bunny” model, simplified according to the Hoppe algorithm (30% of original according to the Hoppe algorithm (30% of original data, processing time - data, processing time - 158.989 sec)158.989 sec), ,

(b) Simplified model (30%) by using simple geometric (b) Simplified model (30%) by using simple geometric error metric error metric

(c) Simplified model according to our approach (30%, (c) Simplified model according to our approach (30%, processing time - processing time - 59.737 sec)59.737 sec)

(a) (a) (b)(b) (c)(c)

Animation with CSRBFs Animation with CSRBFs

The space mapping technique is applied in 3D The space mapping technique is applied in 3D space and can serve for computing of surface space and can serve for computing of surface transformations according to the user demands transformations according to the user demands

• The left image shows the “Lion-dog” model (courtesy of Yutaka The left image shows the “Lion-dog” model (courtesy of Yutaka Ohtake and A Belyev of Max-Planck-Institut für Informatik) Ohtake and A Belyev of Max-Planck-Institut für Informatik) (24930 vertices, 50000 polygons), whose surface was generated (24930 vertices, 50000 polygons), whose surface was generated from range data from range data

• The right image shows plausible deformations after applying The right image shows plausible deformations after applying space deformations by two 3D points (the time required to space deformations by two 3D points (the time required to calculate deformations is about 0.0001 seconds)calculate deformations is about 0.0001 seconds)

Example of global reconstruction. Example of global reconstruction. Pattern dependent reconstruction Pattern dependent reconstruction

contour mapscontour maps • Existing contour maps are still a rich source of dataExisting contour maps are still a rich source of data for for the the description of terrain surfacesdescription of terrain surfaces

• Provide Provide reconstruction of scattered datareconstruction of scattered data

• Main techniques:Main techniques: FEM as a numerical approach to reconstruction of scattered dataFEM as a numerical approach to reconstruction of scattered data FFractal-based surface erosion to mimic appearance of natural terrain ractal-based surface erosion to mimic appearance of natural terrain

surfacessurfaces

Example of global Example of global reconstruction. Pattern reconstruction. Pattern

dependent reconstruction dependent reconstruction contour maps (Cont.)contour maps (Cont.)• Approximation of Approximation of fractalizedfractalized surface (17 contour surface (17 contour

lines), lines), = = 0.1. 0.1.

• Approximation of fractalized surface (255 contour Approximation of fractalized surface (255 contour lines),lines), 0.1 0.1. .

Local reconstruction Local reconstruction Implementation of the partition of unity for Implementation of the partition of unity for

generation of polygons from scattered data of (the generation of polygons from scattered data of (the fragment of Mount Bandai): (a) a curvature analysis. fragment of Mount Bandai): (a) a curvature analysis. Blue area – the surface variation Blue area – the surface variation > 0.3; > 0.3;

(b) result of reconstruction (ray tracing). Number of (b) result of reconstruction (ray tracing). Number of scattered points - 10000, number of vertices after scattered points - 10000, number of vertices after reconstruction – 90000, processing time – 0.941 sec; reconstruction – 90000, processing time – 0.941 sec;

(c) fragment of the mesh as a wire-frame with color (c) fragment of the mesh as a wire-frame with color attributes in accordance with calculated heights attributes in accordance with calculated heights

Examples of shape Examples of shape triangulations by the use of triangulations by the use of

particlesparticles (a) The “Head” model, implicit (a) The “Head” model, implicit

function constructed by CSRBFs, function constructed by CSRBFs, and a final distribution of particles and a final distribution of particles

(b) Polygonization of “Head” (b) Polygonization of “Head” model using final distribution of model using final distribution of particles (1487 points) particles (1487 points)

(a) Incomplete polygonization of (a) Incomplete polygonization of the “Seashell” model, obtained by the “Seashell” model, obtained by using Bloomenthal’s algorithm using Bloomenthal’s algorithm

(b) Complete polygonization, (b) Complete polygonization, obtained by using particle system obtained by using particle system

Example – Local reconstruction Example – Local reconstruction (cont.)(cont.) Surface reconstruction of a technical data set: Surface reconstruction of a technical data set:

(a) cloud of points, 4100 scattered points are used(a) cloud of points, 4100 scattered points are used (b) simplified mesh shaded(b) simplified mesh shaded (c) a fragment of the mesh as wire-frame, 7141 (c) a fragment of the mesh as wire-frame, 7141

verticesvertices

(a)(a) (b) (b) (c)(c)

Improvement of mesh qualityImprovement of mesh quality If a mesh is created for FEM If a mesh is created for FEM

applications, it is very important to applications, it is very important to control the mesh gradation smoothness. control the mesh gradation smoothness. Shape elements have a strong influence Shape elements have a strong influence on discretization errors on discretization errors

(a) (b)(a) (b)(a)(a) Fragment of an initial mesh (“Horse” model)Fragment of an initial mesh (“Horse” model)(b)(b) After improvementAfter improvement

GUI and haptic visualizationGUI and haptic visualization

GUI and haptic visualization GUI and haptic visualization (Cont.)(Cont.)

Engraving operations with haptic feedbackEngraving operations with haptic feedback The main problem is to provide a system response with the speed 0.003 sec.The main problem is to provide a system response with the speed 0.003 sec. RemarksRemarks The virtual environment even with a haptic feedback does not provide a feeling of depthThe virtual environment even with a haptic feedback does not provide a feeling of depth Decartes`s dualism (1664) :Decartes`s dualism (1664) : The intention comes from the The intention comes from the

soul and is used in combination with the information provided soul and is used in combination with the information provided by the senses to determine the proper bodily movementby the senses to determine the proper bodily movement

The second and possibly the greatest problem is that visual The second and possibly the greatest problem is that visual appearance or result of applying cutting operations depends appearance or result of applying cutting operations depends on lighting or observer positionon lighting or observer position

GUI and GUI and Deformations by the use of Deformations by the use of CyberGloveCyberGlove

shape modeling

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