1. 1cs426-winter-2008 Notes  More papers to read: T. Duff, "Compositing 3-D rendered images", SIGGRAPH 1985 R. Cook, "Distributed ray tracing", SIGGRAPH 1984 R. Cook, L. Carpenter, E. Catmull, "The Reyes image rendering architecture", SIGGRAPH 1987

2. 2cs426-winter-2008 Gauss-Newton  For nonlinear least-squares…  Can approximate the nonlinear term with a linear function (Taylor series with the Jacobian!) and get a linear least squares problem: Gauss-Newton  Much more efficient, though we need to solve a (small) linear system to get the direction

3. 3cs426-winter-2008 Evaluating Jacobians  Simplest approach in code: numerically approximate with a finite difference  Can also work out derivative analytically by hand (a little painful)

4. 4cs426-winter-2008 When to stop  In our case, absolute minimum of f(.) is zero: stop when it’s smaller than some tolerance  It might be impossible to get to zero, but at the minimum  f=0: stop when |  f| is small enough  Or give up when maximum number of iterations reached

5. 5cs426-winter-2008 Character Rigging  A “rig” is a model together with a UI for posing it  At its simplest, a skeleton with joint angles available for motion curves  May simplify DOF by enforcing relationships between joints E.g. hand and fingers  May define standard poses (especially for facial expressions!) that can be mixed together Then can set sliders to, say, 70% happy, 20% surprised, … Take weighted linear combination of pose angles

6. 6cs426-winter-2008 What’s left?  We now have the basics of animation  Plan for rest of course: Rendering animations (Semi-)automatic animation  Dynamics for rigid bodies  Particle systems  Skinning, morphing, blending  Motion capture  Motion control

7. 7cs426-winter-2008 Compositing  Visual effects work usually involves combining real footage with CGI: compositing  In fact, even in pure CG shots, films break down each frame into a number of layers that are assembled More flexibility to quickly change the look of a shot Better division of labour

8. 8cs426-winter-2008 Atop  The simplest (useful) and most common form of compositing: put one image “atop” another Image 1 (RGB) on top of image 2 (RGB)  For each pixel in the final composite, need to know what RGB value to take Where image 1 is opaque, choose RGB 1 Where image 1 is “empty”, choose RGB 2 Where image 1 is partly transparent, or where image 1 only covers part of the pixel?

9. 9cs426-winter-2008 Alpha  We add another channel, alpha: RGBA  Encodes whether the pixel of the image is empty (alpha=0) or opaque (alpha=1) or something in between (0<alpha<1) Most important case: at the edges of objects  When we render a layer, we compute and save alpha along with RGB Or if it’s real action, use a “blue screen” behind the actors, estimate alpha  Premultiplied alpha: instead of storing regular RGB + alpha, store rgb=alpha*R, alpha*G, alpha*B and alpha Simplifies formulas to come