CSE 470 Introduction to Computer Graphics Arizona State University Lighting CSE 470 Introduction to Computer Graphics Arizona State University Dianne Hansford

Lighting Overview Elements of a lighting model The Phong illumination model Application of the Phong model Shading methods: flat, Gouraud, Phong OpenGL aspects

Perception of an object influenced by: light sources: number, type, color reflections material properties: reflection & absorption of light 3D feel – depth perception CG: approximate real-world lighting with a model

CG Lighting Models Local Single interaction of light & objects Phong illumination model Global Multiple interaction of light & objects raytracing or radiosity

Elements of the Phong Model Light Source Properties ambient light diffuse light specular light point source vs spotlight positional vs directional

Light Source Properties ambient light scattered, no detectable direction backlighting in a room diffuse light directional, scatters once hits object, closest to the color of light specular light directed and bounces off object in preferred direction plays a role in shininess

Elements of the Phong Model Material (object) properties influences interaction with light 1. reflectance of light a. ambient b. diffuse c. specular d. translucent (opaque) 2. surface normals 3. emissive color

Material Properties ambient reflectance amount of ambient light most visible where no direct light hits diffuse reflectance degree of scattering of light on surface matte vs flat paint finish specular reflectance degree of mirror-like quality

Light & Material Properties Examples increasing diffuse increasing ambient increasing specular

Light & Material Properties absorption/reflectance influence on color Example: red ball will reflect red light absorb green and blue light white light illuminating a red ball  red ball green light illuminating a red ball  black ball

Notation: Light Properties Model is computed independently for red, green, blue components Light’s luminance represented by boldface vectors: La := ambient Ld := diffuse Ls := specular % of full intensity r g b Each vector takes form

Notation: Material Properties Material’s properties represented by boldface vectors: ka := ambient kd := diffuse ks := specular % of reflection of light source’s corresponding property r % g % b % 0 <= r,g,b % <= 1 Each vector takes form

Math of the Phong Model Primary geometry v p point on surface l light – p vector n normal to surface r reflection vector v viewpoint – p vector theta angle of incidence phi angle between v and r p Recall: angle of incidence equals angle of reflection All vectors normalized

Phong Model in OGL vertex color = material emission‡ + (global ambient light scaled by material ambient property) + (ambient, diffuse, specular of lights, attenuated by material properties, viewer location and light position) ‡ at vertex

Diffuse Intensity Calculation Lambert’s Law: light reflected is proportional to the cosine of the angle (theta) between surface normal n and light vector l theta is called the angle of incidence

Diffuse Intensity Calculation Id := intensity of reflected diffuse light Id = kd x Ld x cos(theta) cos(theta) = l • n angles 0 90° Id = kd x Ld x (max{l • n, 0}) “x” is not cross product 3 separate scalar products “• “ is dot product Note: independent of viewer

Specular Intensity Calculation Is := intensity of reflected specular light Basic idea: Is = ks x Ls x cos^s(phi) cos(phi) = v • r r = [2(l•n)]n - l phi = 0°  full specular |phi| > 90°  no specular (never compute angle directly) Focus of specular influenced by s Note: depends on viewpoint

Specular Intensity Calculation s: Phong constant or “shininess” coefficient cos^s(phi) s=0.1 spread s=1 s=10 focus - 90° 90°

Specular Intensity Calculation Blinn-Torrence modification – simplification for faster computation h = (l + v) / || l + v || “halfway” vector cos(alpha) = h • n alpha ~ ½ phi so good approximation

Specular Intensity Calculation Is = ks x Ls x [max{h • n, 0}]^s if l • n < 0 then Is = 0 (no diffuse, no specular)

Attenuation Function For a positional light ... d := distance of light source to vertex ogl choices for functions constant linear quadratic f(d) = 1/a f(d) = 1/(a + b*d) f(d) = 1/(a + b*d + c*d^2) inverse distance functions  diminish intensity d increases for directional light, f(d) = 1

Spotlight Effect c Cone-shaped spotlight defined by: gamma c position gamma “cut-off” angle d direction d sp := spotlight effect for a light source defined by angle between -l and d : cos(delta) = -l • d if delta > gamma sp = 0 else sp = (max{-l • d, 0})^p p influence similar to Phong constant; focus of intensity

Putting It All Together Phong Model I := intensity at a vertex e := emission intensity at a vertex Ma := ambient intensity for the entire model I = e + (ka x Ma) + for each light { [f(d) * sp * (ka*La + Id + Is)] } Remember: boldface indicates r,g,b values

Shading Methods Phong model  color of vertex Shading methods  color of triangle Methods: Flat shading Gouraud (smooth) shading Phong‡ Shading in ogl Recall: triangle normal .vs. averaged vertex normal ‡ confusing, but different from Phong illumination model

Flat Shading One normal per triangle Simulates viewer and light source distant then v, n, l same over triangle  one shading calculation

Gouraud (smooth) Shading One normal per vertex Lighting calculation made at each vertex  I1, I2, I3 Lighting at any point p within triangle v1, v2, v3 I = b1*I1 + b2*I2 + b3* I3 where b1, b2, b3 are the barycentric coordinates of p wrt v1, v2, v3 p = b1*v1 + b2*v2 + b3*v3 (b1 + b2 + b3 = 1)

Phong Shading One normal per vertex ... however a normal is calculated for each rendered point p in triangle vertex normals n1, n2, n3 p = b1*v1 + b2*v2 + b3*v3 n = b1*n1 + b2*n2 + b3*n3 Calculate intensity at p wrt n

Resources Many figures for these slides were taken from Pascal Vuytsteker’s website: http://escience.anu.edu.au/lecture/cg/Illumination/index.en.html Delphi3d’s Phong for dummies http://www.delphi3d.net/articles/viewarticle.php?article=phong.htm

Material Properties

Material Properties