Review! Sphere details (H&B, 602) May be helpful for grad version of A6. Refraction caustic Reflection Details

n^ P = P0+s u ^s ^r

P0

sˆ + rˆ = knˆ and nˆ • sˆ = nˆ • rˆ |P -P |=r u c nˆ • sˆ + nˆ • rˆ = k ⇒ k = 2nˆ • sˆ So rˆ = 2(nˆ • sˆ )nˆ − sˆ Henrik Jensen, http://www.gk.dtu.dk/~hwj

May be helpful for May be helpful for Sphere details (H&B, 602) grad version of A6. Sphere details (H&B, 602) grad version of A6. Refraction Details

+ − = 2 + + = P0 su Pc r Recall that if: as bs c 0 Index of refraction, n, is the θ ratio of speed of light in a i ∆P + su = r vacuum, to speed of light in 2 medium. ()∆P + su •() ∆P + su = r 2 The “discriminant ” is: b − 4ac

∆P• ∆P − r 2 + 2s∆P • u + s2u• u = 0 Typical values: −b ± b2 − 4ac air: 1.00 (nearly) The solution is: s = water: 1.33 The last expression is easily solved using the quadratic 2a glass: 1.45-1.6 n sin θ = n sin θ i i r r θ equation. If the discriminant is negative (complex diamond: 2.2 r solutions), then the ray does not intersect the sphere. Note that in the book, u is a unit vector, so u•u=1, thus a=1, and b has a factor of 2 that is removed by dividing by 2a=2, The indices of refraction for the two media, and the incident to get equation 10 -71. θ θ angle, i , yield the refracted angler . (Also need planarity). Surface detail Surface detail, II

• Texture maps: – Make albedo (or color) a function of position in • Bumps these coordinates – we assume that the surface has a set of bumps on it – Rendering: when intersection with a casted ray is • e.g. the pores on an orange found, compute coordinates and get albedo from a – these bumps are at a fine scale, so don’t really affect the map point of intersection with casted rays, but do affect the – This is not specific to ray-tracing normal – strategy: • obtain normal from “bump function” • shade using this modified normal • notice that some points on the surface may be entirely dark • bump maps might come from pictures (like texture maps) From RmanNotes: http://www.cgrg.ohio-state.edu/~smay/RManNotes/index.html

Surface detail, III

• A more expensive trick is to have a map which includes displacements as well • Must be done before visibility

From RmanNotes From RmanNotes: http://www.cgrg.ohio-state.edu/~smay/RManNotes/index.html http://www.cgrg.ohiostate.edu/~smay/RManNotes/index.html