1. ATEC 6351.001 Procedural Animation Introduction to Procedural Methods in 3D Computer Animation Dr. Midori Kitagawa

2. In class  Pay attention  Take notes  Learn  Be ready for a pop quiz

3. Week 9: Mapping  Texture mapping  Texture coordinates (UV coordinates)  Two-part texture mapping  Aliasing & anti-aliasing  Mip-mapping  Bump mapping  Displacement mapping  Solid (procedural 3D) texture

4. Texture mapping  Process of projecting a 2D texture image onto the surface of a 3D object.  2D image can be: a pre-prepared source image (a photo, a painting, etc.) in an image file or a procedurally created image

5. Texture mapping  can manipulate a variety of surface characteristics, such as color, transparency, specularity, incandescence, bumpiness, and displacement.

6. How?  How do we create a corresponding relationship between a 3D object and a 2D image?

7. Texture coordinates  In order to apply 2D texture to a 3D object, we create texture coordinates.  Texture mapping coordinates in texture space are represented as (U, V).

8. NURBS and Bezier  Surface patch (e.g., NURBS and Bezier) is a rectangular patch with UV coordinates.  So, it is natural to use a NURBS surface's UV coordinates as texture mapping coordinates.

9. How about polygons?  Polygons have arbitrary numbers of vertices and shapes.  How can we make texture mapping coordinates for each vertex of a polygon?

10. Two-part texture mapping  Create texture coordinates in two steps: Step 1. A 2D texture is mapped onto the surface of a regular 3D geometric shape, such as plane, cube, cylinder, and sphere. Step 2. A 3D texture (created in Step 1) is mapped onto the surface of an arbitrary shaped object.

11. Two-part texture mapping  Commonly used two-part mapping methods are: Orthographic (flat, planar) projection Cylindrical projection Spherical projection

13. Texel and pixel  Pixel is the smallest element in a digital image.  Texel is the smallest element in a texture mapping source image.  When a large texture area corresponds to a small image area, a large number of texels need to be mapped to a single pixel.

14. When a large texture area corresponds to a small image area, a large number of texels need to be mapped to a single pixel.  For instance, in a perspective view of a plane with a texture mapping, a single pixel in a rendered image may correspond to thousands of texels in the source image. Source image Rendered image

15. When a large texture area corresponds to a small image area, a large number of texels need to be mapped to a single pixel.  If you use the color of a single texel to paint the pixel (i.e. point sampling), aliasing occurs.

16. Aliasing

17. How to avoid aliasing?  Average the colors of all the corresponding texels to paint a pixel?

18. Averaging the colors of all the corresponding texels…  A single pixel in a rendered image may correspond to thousands of texels in the source image.  If the renderer had to average the colors of all the corresponding texels per pixel, it would take a lot of rendering time.  Bad idea.

19. Mip-mapping  Texture mapping method that prevents aliasing without making rendering take much longer.  The renderer prepares pre-filtered mip- mapped textures before starts rendering.

20. Mip-mapped texture  Multiple copies of an original texture mapping image, all derived by averaging down the original image to successively lower resolutions.  Each image in the sequence is at exactly half the resolution of the previous. The red, green, and blue components of a texture mapping image are separated to create a titled square map

21. Mip-mapping  During the rendering process, the appropriate level of texture image is selected, depending on how much screen coverage there is and how obliquely the object is being viewed.  The further away or more obliquely the object is, the lower-resolution (i.e., blurrier) version of the texture is used to render it.

22. Mip-mapping  Many 3D applications (e.g., Houdini and Maya) use the mip-mapping technique and rendering takes less time if you use square textures.  If your texture is not square, add black borders to make it a square texture.  A multiple of 2 (e.g.,1024 x 1024) is the best choice for a resolution.

23. Bump mapping  gives a bumpy appearance to a flat surface by disturbing the surface normals (normal vectors) of a surface

24. Bump mapping  The bumpiness of bump mapping does not appear in the silhouette (profile edges) of an object.

25. Displacement mapping  modifies both the position and surface normal at each point on a surface, giving bumpiness to the silhouette of an object as well.

26. Displacement mapping  gives bumpiness to the silhouette of an object.

27. Solid (3D procedural) texture  provides texture to the 3D space in which an object exists.  The object's color at each point on the object surface is determined by where the point is in the solid texture.

28. Solid (3D procedural) texture  Solid textures are good at creating an object that seems to have carved out of a textured material, such as wood and marble.

29. Solid (3D procedural) texture  When an object with a solid texture is deformed in an animation sequence, the texture on the object appears to change (or slip) over time unless you bake the texture to the object.