Surface displacement, tessellation, and subdivision. Ikrima Elhassan. Overview. The Reyes image rendering architecture ", Cook et al., SIGGRAPH 1987 Curved PN triangles ", Vlachos, Peters, Boyd, and Mitchell, Symposium on Interactive 3D Graphics, 2001 . Reyes Architecture: Support Goals.
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Surface displacement, tessellation,and subdivision
Texture locality & filtering
Ease of Clipping & Displacement maps
Shading occurs on nonvisible micropolygons
Rendering time becomes tied to depth complexity
No inverse calculations
No clipping calculations
No texture thrashing and can eliminate run time filtering
Sampling occurs after shading
Difficult to handle metaballs
Hard to bound primitives such as particle systems for bucket sort
Polygons don’t have natural coordinate system
Use barycentric coordinates for triangular domain
Consider a set of points P0, P1,…, Pn, and consider the set of all affine combinations taken from these points. That is all points that can be written as
This set of points forms an affine space, and the coordinates
are called the barycentric coordinates of the points of the space.
Recall that a point within a triangle Δp0p1p2, can be described as p(u,v) = p0 + u(p1-p0) + v(p2-p0) = (1-u-v)p0 + up1 + vp2, where (u,v) are the barycentric coordinates
Bicubic interpolation results in C2 surfaces
Given a tabulated function yi = y(xi), i = 1...N , focus attention on one particular interval, between xj and xj+1. Linear interpolation in that interval gives the interpolation formulay = Ayj + By(j+1)
If we have yi”, we can add to the right-hand side of equation a cubic polynomial whose second derivative varies linearly from a value y j on the left to a value y (j+1) on the right.
Saves bandwidth and memory
Curved surfaces and better shading
Cant control curvature
No sharp edges