research goal we provide physical visualizations to modern structural biologists, thus reviving...
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Research Goal We provide physical visualizations to modern structural
biologists, thus reviving tactile feedback, in addition to immersive environments.
Embed multiple representations within a single form:- Create a solid model by combining a backbone spline
model with converted molecular spline surface, originally a triangular mesh
- Fabricate the solid model using Stratasys Fused Deposition Model (FDM) Rapid Prototyping Machine
- Create a flexible mold from the FDM model- Use Z-Corp 3D Color Printer to create an opaque color
coded backbone - Insert the backbone into the flexible mold and inject
clear plastics to fill the remaining volume
Research Challenges Modeling software packages require homogenous
representations in order to combine models. Develop methods to achieve smooth transitions where
spline surfaces meet along edges. Some corners may not be able to be represented smoothly.
Research Solutions Develop a system to convert molecular meshes into spline
models Introduce a novel algorithm that:
Makes all edges smooth except near corners Minimizes G1 discontinuities that may occur near
corners at which surfaces meet.
Conversion System Pipeline
Conclusion
Corner Stitching Algorithm
Overview
Joel Daniels IIElaine Cohen
Acknowledgements
References
This work was supported in part by NSF(EIA0121533) and NIH(573996).
[1] Sanner, M., 1999. “Python: A programming language for software integration and development”. J. Mol. Graphics Mod., 17, February, pp. 57–61.[2] M. Sanner, B. Duncan, C. C., and Olson, A., 1999. “Integrating computation and visualization for biomolecular analysis: An example using python and avs.”. Proceedings Pacific Symposium in Biocomputing, pp. 401–412.[3] M. Sanner, D. S., and Olson, A., 2002. “Viper a visual programming environment for python”. 10th International Python Conference, February.[4] Cohen, E., Riesenfeld, R., and Elber, G., 2001. Geometric Modeling with Splines: An Introduction. AK Peters, Ltd.[5] Loop, C., 1994. “Smooth spline surfaces over irregular meshes”. In SIGGRAPH ’94: Proceedings of the 21st annual conference on Computer graphics and interactive techniques, pp. 303–310.[6] Krishnamurthy, and Levoy, M., 1996. “Fitting smooth surfaces to dense polygon meshes”. In ACM Transaction on Computer Graphics (SIGGRAPH 1996 Proceedings).[7] Livingston, J. B., 1990. “Intersurface continuity of solid models”. Master’s Thesis, University of Utah, Department of Computer Science.
The system successfully converts a molecular mesh into a spline model, creating homogenous environments in which modeling software packages can operate. Leads to being able to produce the desired physical
visualizations. Converted model an accurate representation of the
original data, via interpolation, with an added level of smoothness.
A novel corner stitching algorithm is introduced, minimizing creases along boundaries.
Potential ridges are confined to the first and last knot interval for each boundary. These ridges constitute a small portion of the overall
boundary area, and even smaller portion of area of the overall model.
99% of the boundaries of the flatter model are within 1o of G1 continuity. Even in a worse case, as with the high curvature model, similar results are realized as 98% of the boundary curve is within 1o of G1 continuity.
Comparisons of the original and converted models demonstrate that even the worst case ridge is significantly smoother than the original dihedral angle.
1. Fit a cubic surface to the neighborhood data points of the corner.
2. Compute the tangent vectors on this surface along each boundary emanating from the corner.
3. Compute cross-boundary information at the corner to optimize smoothness. Constraints include:a. Co-planarity of differential properties.b. Regularity of parameterized corner region.
Case Studies/Results
Quality Guarantee
Ridges are sections of a boundary curve where the surface normals of the two abutting surfaces differ.
Our algorithm picks a solution that confines these regions to corners and minimizes the ridges without modifying the data or adding degrees of freedom.
Two models are analyzed, measuring all ridges that occur in the conversion process. The peak to trough variation is less steep in the model A than in model B, especially in areas surrounding corners.
The graphs plot the difference in degrees between the normals of two surfaces along their shared edge.
The ridges are shown as G1 discontinuities, where the difference of the normals is not 0 degrees.
The algorithm confines the trouble regions to shared boundary curves between the corner and first shared data point.
I. Model Ai. Worst case angle = 1.74o
i. corresponding boundary on the original mesh = 7.6o
ii. 92% of the boundary is G1 continuousiii. 99% of the boundary is within 1o of G1 continuity
II. Model Bi. Worst case angle = 4.48o
i. corresponding boundary on the original mesh = 12.4o
ii. 91% of the boundary is G1 continuousiii. 98% of the boundary is within 1o of G1 continuity
1. The input triangular mesh is a byproduct of molecular sampling techniques. Resulting in large meshes with many data points.
2. The triangles of the mesh are mapped to the faces of the icosahedron, and these faces are paired to form the rectangular data grids
3. Cross-Boundary smoothness is guaranteed in the estimation of differential properties across adjacent data grids.
4. Corner tangents and twists are computed to minimize G1 discontinuities.
5. Complete spline interpolation converts the data grids and tangents into a smooth spline model.
6. Modeling software packages combine models to form a solid model within a homogenous environment.