Lecture #16 -- Wed 10/21, 2009.

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**What are the key differences between the way that Wei and Levoy put texture on a surface**

and the way that you are supposed to do it in the current programming Assignment ?

**Could you modify the****Wei and Levoy scheme so that**

the result maintains the full symmetry of your genus-4 object ?

The texture coordinates applied to the original polyhedron are simply subdivided in the proportion of the topological splits executed.

Problems may arise in assigning texture coordinates, if the surface is not a simple cylindical or toroidal domain.

Whenever the genus of a surface is different from 1, then you cannot regularly tile this surface with quad tile with all valence-4 vertices.

A cube has eight valence-3 vertices, and one geometrical vertex will have to carry different texture coordinates for different faces,

(thus it might be better to carry the texture coordinates with each face, rather than on a shared vertex).

To model a "spherical" ball we may start with a simple cube; but the "cubist" fish shape will extend beyond a single face and overlap into two adjacent faces.

Since these pieces belong to some other fish, they be be of different colors; different cube faces may have different combinations of colors.

Thus, multiple copies of one B&W texture outline, filled with different colors, are needed for the different sides of the cube.

On the cube itself, the texture coordinates will then have to be rotated so that a seemless connection between the different patterns and colors occurs.

In some cases, some of the tiles may also have to be mirrored! (

Here is another textured example of genus 2. -- And another one of genus 3.

More complex examples of a genus 5 surface are discussed here.

Here are some actual, Escher-tiled objects,

Escher tiling with 12 lizards(tetrahedral symmetry) |
Escher tiling with 24 birds(octahedral symmetry) |
Tiling with 60 butterflies(icosahedral symmetry) |
48 starfish on genus-7 surface |

**What is the underlying representation for Minimum-Variation Surfaces ?****What are the various (nested?) loops of the optimization process ?****How are G1- and G2-continuity enforced ?**

Send me: a pretty picture, an updated description of your encoding scheme and your data structures,

and a brief discussion of some of the design choices you have made.

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