feature-based 3d morphing based on geometrically constrained sphere mapping optimization

Feature-based 3D Morphing based on Feature-based 3D Morphing based on Geometrically Constrained Sphere Geometrically Constrained Sphere

Mapping OptimizationMapping Optimization

Theodoros AthanasiadisTheodoros Athanasiadis

Ioannis FudosIoannis Fudos

[email protected]

[email protected]

Department of Computer Science

University of Ioannina, Greece

University of Ioannina SAC 2010March 2010

How? Morphing

A novel editing paradigmA novel editing paradigm

Mimic the way an artist shapes a sculpture. Start from a volume

or object that is close to the intended target and iteratively

shaping (morphing) its parts to finally render what the artist had

in mind.

Initial motivation: make CAD design process accessible to users with no previous CAD/CAM software experience.

Final Goal: To offer a novel editing paradigm for CAD modelsbeyond traditional CAD editing of mechanical parts.



Issues that arise:

Accuracy: We may need to enforce geometric constraints to ensure

the intended accuracy. Thus, we need a morphing technique that

can be combined with other geometric constraints.

Robustness: The morphing process has to be robust, with no in-

between invalid morphs.

Local control: Compatibility with feature-based design.



Issues that arise:

Support user-defined constraints: Feasible. In some cases we have

managed to incorporate in the morphing process. Work in progress.

Efficiency: Needs to be addressed more carefully to support

interactivity.


IntroductionIntroduction

Goal: unsupervised robust 3D morphing of arbitrary genus-0 polyhedral

objects.

Based on a sphere mapping process that

maintains the correspondence among the initial polygons and the

mapped ones

while preserving topology and connectivity.

A fully automated feature-based technique that

matches surface areas (feature regions) with similar morphological

characteristics between the two morphed objects and

performs morphing according to this feature region correspondence list.


Feature Based Morphing for CAD

Introduction

Topology preserving mapping on the 3D sphere

Surface correspondence and interpolation

Feature detection, matching, mapping and morphing

Examples and performance evaluation

Talk OverviewTalk Overview


Morphing Overview

An initial bijective mapping is computed for each object on the unit sphere

with either thermal conduction or laplacian smoothing.

The Initial mapping optimized by using constraints and a target function.

The projections are combined and a merged topology is computed.

The merged topology is mapped back to the original models with the use of

barycentric coordinates.

The models are interpolated on the GPU (linear interpolation may be used).


Topology Preserving Mapping on the 3D Sphere

Initial mapping using (i) thermal conduction (ii) laplacian smoothing

Initial mapping optimized by using constraints and a target function.


Initial Mapping by Laplacian Smoothing

Map each vertex on the unit sphere:

Use iteratively the following area weighted version of laplacian

smoothing on the unit sphere:

5 Iteration intervals


Sphere Mapping Optimization

Constraints:

keep on unit sphere

maintain topology

Target function for optimization:


Sphere Mapping Optimization

Final result of mapping the Blender monkey. Initial characteristics are

preserved



Introduction







Surface Correspondence and Interpolation

Deriving the merged topology

Linear or other more appropriate interpolation.

Implementation of the GPU for real time morph animation.

The user may easily select the appropriate morph.



Introduction







Feature-based Morphing

Use user defined CAD features or detect feature regions of potential

interest

For automatic detection we use concavity intensity variations and normal

vector rapid changes.



We build an adjacency graph for the feature regions, the edges are

labeled by the geodesic distances of the centroids of the feature regions.

Then we eliminate edges with large geodesic distances.

Small regions that can contribute to noise are merged.



Original graph of first head mesh

Reduced graph



Match the three highest degree nodes and align the models.

The remaining graph nodes are matched based on their

degree,

distance and

covered area similarity:

A list of feature point pairs is extracted

An example of detecting feature regions in two dead meshes.

Feature point matchingFeature region matching



Constraints:

keep on unit sphere

maintain topology

preserve edge length

Target function for optimization:

Optimized mapping for one object is performed as before, for the

other we go on as follows:


Feature-based Morphing Algorithm Overview

NL Optimization

perform material, normals etc calculations in the GPU each frame

Initial Projection of the first model

Initial Projection of the second model

NL Optimization

Merged Topology

Feature NL Optimization



Introduction







Simple Morphing vs. Feature-based Morphing


Examples and Performance Evaluation

Morphing with 3D alignment and feature point matching.



Morphing with alignment but no feature point matching: fish (4994 faces) to duck (1926 faces), merged topology has 28526 faces.

Morphing with alignment and feature point matching: fish (4994 faces) to duck (1926 faces), merged topology has 33038 faces.


Demo Video: Morphing



Optimization is too slow. Solutions: GPU implementation (open)

Simple morphing is ok, since mapping may be part of the representation.In feature-based morphing it has to be computed for each pair of objects.


Conclusions

Novel approach to morphing that provides a robust, universal, easy to implement method for structural 3D morphing between genus-0 polyhedra.

Can be generalized to non genus-0 objects (previous approaches are applicable to our technique).

Slow mapping optimization phase.

Method is compatible with feature-based CAD models.

Allows for editing of free form CAD models.

Work in progress: combine with user define constraints (intra feature constraints), use user defined constraints to perform matching among features of different CAD models, utilize feature hierarchy.


Level of Detail with Morphing

Motivation : Morphing techniques can be used to do linear interpolation between the

two closest level of details (like trilinear filtering for textures).

Advantages Each level of detail can have a completely different geometric structure. Additionally remeshing

techniques can be used to further cut down the number of polygons.

The next lod can be a totally different shape. For example, a high poly house model can be just a box in the lowest level of detail. This can be used to achieve interesting visual effects.

The level of details can greatly differ, making a vast difference in the poly count by the use of an inferior level of detail.

Fully accelerated by GPU techniques.

Drawbacks The morphed mesh usually has more polygons (less than 25% increase) Only closed Genus-0 objects can be handled currently (possibility of extension with additional cost)


Lod Example

A high poly mesh (12 K triangles) left, and a low poly mesh (500 triangles) right. The middle model is the linear blend computed automatically with t = 0.5. Original models produced with blender software.

Real time morphing in the vertex shader, left and right images are the original models.

Level 0 t = 0.33 t = 0.66 Level 1


Lod Example Detail

Level 0 t = 0.33 t = 0.66 Level 1 Close up of the morphing sequence reveals the smooth transition from the high polygon model to

the low polygon one.

feature-based 3d morphing based on geometrically constrained sphere mapping optimization

Documents

sphere mapping process

feature based morphing

morphing process

sphere mapping optimizationc

morphing technique

d sphereinitial mapping

featurebased design

unit sphere