Feature-based 3D Morphing based Feature-based 3D Morphing based on Geometrically Constrained on Geometrically Constrained Sphere Mapping Optimization Sphere Mapping Optimization Theodoros Athanasiadis Theodoros Athanasiadis Ioannis Fudos Ioannis Fudos [email protected][email protected]Department of Computer Science University of Ioannina, Greece
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Feature-based 3D Morphing based on Geometrically Constrained Sphere Mapping Optimization Theodoros Athanasiadis Ioannis Fudos [email protected][email protected].
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Feature-based 3D Morphing based on Feature-based 3D Morphing based on Geometrically Constrained Sphere Geometrically Constrained Sphere
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.
University of Ioannina SAC 2010March 2010
A novel editing paradigmA novel editing paradigm
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.
University of Ioannina SAC 2010March 2010
A novel editing paradigmA novel editing paradigm
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.
University of Ioannina SAC 2010March 2010
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.
University of Ioannina SAC 2010March 2010
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
University of Ioannina SAC 2010March 2010
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).
University of Ioannina SAC 2010March 2010
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.
University of Ioannina SAC 2010March 2010
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
University of Ioannina SAC 2010March 2010
Sphere Mapping Optimization
Constraints:
keep on unit sphere
maintain topology
Target function for optimization:
University of Ioannina SAC 2010March 2010
Sphere Mapping Optimization
Final result of mapping the Blender monkey. Initial characteristics are
preserved
University of Ioannina SAC 2010March 2010
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
University of Ioannina SAC 2010March 2010
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.
University of Ioannina SAC 2010March 2010
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
University of Ioannina SAC 2010March 2010
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.
University of Ioannina SAC 2010March 2010
Feature-based Morphing
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.
University of Ioannina SAC 2010March 2010
Feature-based Morphing
Original graph of first head mesh
Reduced graph
University of Ioannina SAC 2010March 2010
Feature-based Morphing
Original graph of first head mesh
Reduced graph
University of Ioannina SAC 2010March 2010
Feature-based Morphing
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
University of Ioannina SAC 2010March 2010
Feature-based Morphing
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:
University of Ioannina SAC 2010March 2010
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
University of Ioannina SAC 2010March 2010
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
University of Ioannina SAC 2010March 2010
Simple Morphing vs. Feature-based Morphing
University of Ioannina SAC 2010March 2010
Examples and Performance Evaluation
Morphing with 3D alignment and feature point matching.
University of Ioannina SAC 2010March 2010
Examples and Performance Evaluation
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.
University of Ioannina SAC 2010March 2010
University of Ioannina SAC 2010March 2010
Demo Video: Morphing
University of Ioannina SAC 2010March 2010
Examples and Performance Evaluation
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.
University of Ioannina SAC 2010March 2010
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.
University of Ioannina SAC 2010March 2010
University of Ioannina SAC 2010March 2010
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)
University of Ioannina SAC 2010March 2010
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
University of Ioannina SAC 2010March 2010
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