4. Results

Figure 4 shows an implementation of the proposed technique using a software rasterizer: A hyrid approach of image-based lighting [6] and standard phong per-pixel lighting [7] has been implemented. The base-sphere consists of about 2500 triangles; the cubemap has been exported from Milkshape [8] using a custom-plugin that takes care of the preprocessing step and directly outputs the grayscale cubemap (8-bits per channel). The software rasterizer is capable of rendering the scene at an average of 14 frames per second on a Pentium IV 2,8 GHz - resolution 320x240. An implementation of the technique on next-gen graphics hardware should run considerably faster; therefore the current software-only implementation should be seen as proof-of-concept.

Figure 4. Screenshots showing the reconstruction of a polygonal model from a scale map.

Figure 5. Skull rendered with reconstructed normals as color.

5. Limitations

Figure 6. Detection of surface-ray intersection points.

While the proposed technique builds a solid base for interpolation between models, it comes with limitations concerning the shape of the source models: The employment of a sphere as base-primitive and the idea of offsetting its vertices along their normals limits this approach to convex models.

In the preprocessing step the original model's surface is scanned by casting rays through the bounding sphere's origin and calculating intersection points with the model's triangles. Although this algorithm works for convex models, because it would detect a single intersection point per ray, it fails when being applied to concave models. Figure 6 illustrates the problem of multiple intersection points.

Because we can only select one of these points for the calculation of the scale factor the overhang of the concave shape could not be captured. The reconstructed model would therefore not resemble the original shape.

Another limitation associated with the presented technique is related to the representable range of surface slopes: Spheres have to be approximated with triangles, which adds a discrete nature to the base-primitive. Because vertices can only be moved along their normal, steep geometric slopes cannot be recreated from the cubemap-data if the base-sphere is not tesselated well enough.

6. Conclusions

This paper presents a technique for model-encoding into cubic scale-maps and the reconstruction of the model including normals. The proposed algorithm greatly simplifies the interpolation of closed, convex polygonal models with different amounts of triangles and vertices through blending between two scale-maps. The technique relies on capabilities available on next-gen graphics cards: programmable vertex units with support for texture sampling (vertex-shader model 3.0). The proof-of-concept implementation was created using a software rasterizer presenting the different aspects of the algorithms.

References

[1] Mitchell, Jason. "Direct3D Shader Models". Presentation at GDC 2004.

[2] Stanford University Computer Graphics Laboratory. "The Stanford Bunny".

[3] Woo et al. "OpenGL Programming Guide, 2nd Edition". pp. 57 - 62. Addison-Wesley, 1997.

[4] Bourke, Paul. http://astronomy.swin.edu.au/~pbourke/modelling/sphere/

[5] Reiter, Stephan. "Muli3D". API version 0.63. http://muli3d.sourceforge.net/

[6] Bjorke, Kevin. "Image-Based Lighting". In GPU Gems, Addison-Wesley, 2004.

[7] Phong, Bui Toung. "Illumination for Computer Generated Pictures". Communications of the ACM, 1975.

[8] Cirgan, Mete. "Milkshape 3D". http://www.milkshape3d.com/