Reflection and Transmission

Transcription

1 Reflection and Transmission Ed Angel Professor of Computer Science, Electrical and Computer Engineering, and Media Arts Director, Arts Technology Center University of New Mexico

2 Introduction Interactions between light and materials Phong model - Absorbtion - Diffuse and specular reflections - Puerely local Reflection: Translucent surfaces - Refraction - Frensel effect - Chromatic dispersion 2

3 Global vs Local Most of these effects can only be computed in a global renderer such as a ray tracer 3

4 Ray Tracing Ray tracers can make use of all these effects in a global calculation by tracing rays R N L T -N 4

5 Environmental Map Can use all these effects Implement in Cg with vertex and fragment programs 5

6 Refraction With pure refraction, all the light is transmitted but the angle of refraction is determined by Snell s law ή l sin θ l = ή t sin θ t where ή l and ή t are the speed of light relative to the speed of light in a vacuum Let ή = ή l / ή t 6

7 Computing T ή 2 sin 2 θ l = ή 2 (1- cos 2 θ l )= sin 2 θ t = 1-cos 2 θ t Solving for cos θ t Assuming normalized vectors cos θ t = T N = (1- ή 2 (1-cos 2 θ l )) 1/2 where cos θ l = T N T, N, and L must be coplanar T = L + N and T T = 1 Solving T = -1/ ή L (cos θ t -1/ ή cos θ l ) N 7

8 Notes Critical angle: total internal reflection 1= ή 2 (1-cos 2 θ l ) Snell s law is a statement that light takes the shortest path (in time) Can apply to reflection maps (see Cg Tutorial) via vertex program 8

9 Fresnel Effect Some light is reflected and some transmitted at surface between two materials Amount of light reflected is greatest at shallow angle Approximation: use affine combination of refracted and reflected colors where = max (0, min(1, bias + scale (1 + L N) power )) 9

10 Chromatic Dispersion The refraction coefficient is actually a function of wavelength N L T r -N T g T b 10

11 Chromatic Dispersion with Cg Easy to do with reflection maps Use three values of Make use of vector operations 11

12 Fragment Program void C7E5v_dispersion(float4 position : POSITION, float3 normal : NORMAL, out float4 oposition : POSITION, out float reflectionfactor : COLOR, out float3 R : TEXCOORD0, out float3 TRed : TEXCOORD1, out float3 TGreen : TEXCOORD2, out float3 TBlue : TEXCOORD3, { uniform float fresnelbias, uniform float fresnelscale, uniform float fresnelpower, uniform float3 etaratio, uniform float3 eyepositionw, uniform float4x4 modelviewproj, uniform float4x4 modeltoworld) 12

13 Fragment Program oposition = mul(modelviewproj, position); // Compute position and normal in world space float3 positionw = mul(modeltoworld, position).xyz; float3 N = mul((float3x3)modeltoworld, 13

14 Fragment Program void C7E6f_dispersion(float reflectionfactor : COLOR, float3 R : TEXCOORD0, float3 TRed : TEXCOORD1, float3 TGreen : TEXCOORD2, float3 TBlue : TEXCOORD3, out float4 color : COLOR, { uniform samplercube environmentmap0, uniform samplercube environmentmap1, uniform samplercube environmentmap2, uniform samplercube environmentmap3) 14

15 Fragment Program // Fetch the reflected environment color float4 reflectedcolor = texcube(environmentmap0, R); // Compute the refracted environment color float4 refractedcolor; refractedcolor.x = texcube(environmentmap1, TRed).x; refractedcolor.y = texcube(environmentmap2, TGreen).y; refractedcolor.z = texcube(environmentmap3, TBlue).z; refractedcolor.w = 1; // Compute the final color color = lerp(refractedcolor, reflectedcolor, reflectionfactor); } 15