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Barycentric Coordinates

B. P( u, v, w). C. A. Barycentric Coordinates. Position on plane of triangle ( u, v, w ) P( u, v, w ) = au + bv + cw (where a, b, c are locations of vertices. u + v + w = 1 2 coords 0  vertex 1 coord 0  edge. B. P( u, v, w). C. A. Barycentric Coordinates.

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Barycentric Coordinates

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  1. B P(u, v, w) C A Barycentric Coordinates • Position on plane of triangle (u, v, w) • P(u, v, w) = au + bv + cw (where a, b, c are locations of vertices. • u + v + w = 1 • 2 coords 0  vertex • 1 coord 0  edge

  2. B P(u, v, w) C A Barycentric Coordinates • If any coordinate is < 0 or > 1, point is outside triangle

  3. Barycentric Coordinates • u = Aa / A where A is area of complete triangle • v = Ab / A • w = Ac / A B Aa Ac Ab C A

  4. Stochastic Ray Tracing • Antialiasing • Gloss – distribute reflected rays • Blurred transparency – distribute transmitted rays • Soft shadows – distribute light rays (to an area source) • Depth of field – distributing locations over lens • Motion blur (moving object or moving camera) – distributing rays over time

  5. Gloss Instead of just a simple reflected ray, shoot more and perturb them. This will take surface from mirror-like

  6. Transparency • Same thing, perturb ray • May also want to try textured transparency • Look up a texture map that describes the transparency (or properties) of the surface. • Screen-door transparency

  7. Soft Shadows • Area light sources • Shoot shadow rays to points on light • Cook suggests distributing rays over light based on brightness of areas of light • Use projected area to weight rays

  8. Camera Models • Pinhole – ideal camera • All rays go through single point • Everything in focus -- unrealistic

  9. More Realistic Model • Lenses with spherical surfaces • Why?

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