# CS770/870 Spring 2017 Color and Shading

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1 Preview CS770/870 Spring 2017 Color and Shading Related material Cunningham: Ch 5 Hill and Kelley: Ch. 8 Angel 5e: Angel 6e: Making the scene more realistic Color models representing the color of materials ighting models representing interaction of light with material color Shading models determining the color of a pixel based on lighting models (usually) mesh shading Gouraud shading Phong shading 02/07/17 2 Color Models We say that objects have color, but it s not quite right light has color objects have material properties that interact with the light that falls on them some of the light that falls on an object is reflected, some is absorbed and some might be transmitted through it we say that an object is green if it reflects only the green wavelength of light and absorbs all others To model color, we need to model light Achromatic ight Achromatic light is gray scale light model only the luminance or intensity (physics terms) or brightness (a psychological term meaning perceived intensity) most important (perceptual) component of light Modeling intensity/brightness Assume human perceptual range can be represented as a value between 0.0 and 1.0 Display device has 256 values for intensity What should the mapping be? 3 4

2 Modeling Intensity Map brightness perception (0.0, 1.0) to hardware intensity (0,255) linear mapping is easy and seems intuitive but it s not right human perception is very non-linear: In 1834 Ernst Weber showed that ΔI/I constant, where ΔI is a noticeable intensity difference (just noticeable difference, or JD) and I is the intensity This breaks down at very low and very high intensities, but logarithmic mapping is much closer to our brightness perception scale ogarithmic Intensity Mapping Assume the device s lowest intensity, I 0, cannot be perceived; that is value 0.0 Assume 1.0 is highest intensity that can be achieved by the device Assume I 1 is value of lowest intensity that can be perceived Want each selected intensity value to be r times the previous: I 2 = I 1 *r, I 3 = I 2 *r = I 1 *r*r,, I 255 = I 1 *r 254 but, I 255 = 1.0 = I 1 *r 254 so r = (1/ I 1 ) 1/254 = I 1-1/ Intensity Mapping Problems Human perception does not match any particular device Different display devices have different dynamic ranges so the mappings will be different. Gamma correction - compare 2 devices behavior in attempt to have both show same image with same end visual effect. Chromatic Color In addition to intensity/brightness, we perceive 2 other aspects of light: hue (dominant wavelength) what we think of as color red and pink and colors between are all reds saturation the purity of the color bright red is called fully saturated as we add white to red, it gets more and more pink 7 8

3 Basic Color Models Hue, saturation, and intensity can be used to model color Red, Green, and Blue can also be used Given pure red, green and blue lights, can represent (most) visible colors by mixing appropriate combinations of them Since most display device hardware is based on mixing red, green, and blue light, we ll use this model first. Modeling ight ight in a scene ambient light no explicit source; collection of all secondary light beams bouncing around point light sources light that appears to emanate from an infinitely small point at a particular location; casts hard shadows area/volume light sources light that emanates from a light source with a nonzero area or volume; casts soft shadows 9 10 Models for Direct ight Ambient light (constant color) Each object (or face of an object) has some constant color throughout the face: reflection of ambient Reflection diffuse reflection: matte appearance specular reflection: shininess Transmission: light passes through a semitransparent surface diffuse transmission: not usually modeled specular transmission: light bends as it passes through the surface Ambient ight ight in the scene with no identified source Efficiently models the light that bounces around scene from all light sources User specifies ambient light in the scene: I a For each surface, user specifies the color and percentage of ambient light reflected by that surface: k a * C a * I a where C a and I a are r,g,b triples (vectors) and k a is % as fraction Can also let each light contribute to the ambient light: k a *C a * Ia Sometimes the constant k a is folded into the C a vector

4 Diffuse Reflection ambert s law for a perfect diffuser material light from a light source is reflected from any point on the surface of a perfect diffuser equally in all directions; surface modeled as infinitely many microfacets aimed randomly in all directions amount of reflection is based on the cosine of the angle between the surface normal at the point and the vector from the point to the light. θ if and are unit vectors I d = k d * C d * I * where = cos θ = cos θ and k d is diffuse coefficient and C d is the diffuse reflection color of the surface. early always, C d = C a Diffuse Reflection Revealed Consider a beam of light as a cylinder with base area d It illuminates a surface area, d/cosα Can also say an area, da, of the surface is lit by a cross section of the light beam of area da*cosα For a perfect diffuser the same number of photons will be reflected from da towards the viewer regardless of the location of the viewer d d/cosα da*cosα da Specular Reflection Shininess Coefficient ear the direction of principal reflection, shiny surfaces reflect the color of the light more than the color of the surface Phong modeled this with a shininess coefficient, n, in the formula below: R is dir. of principal reflection R = 1 V points at viewer, V = 1 points at ight source α β α V R I s = k s * C s * I * (V R) n where C is the specular color of the surface. Usually C s = I (or 1,1,1) so that only reflected light seen but there are exceptions. The n coefficient raises the cosine (V R) to a power What effect does it have? As n gets larger, cos n gets narrower. shiny highlight gets smaller ote that the brightness does not change 15 16

5 Specular Transmission Specular transmission can only be modeled in the context of the visible surface algorithm used to determine what is visible. We ll come back to it when we talk about the z- buffer algorithm and ray tracing Phong ighting Model The basic lighting model is due to Bui Tuong Phong: Given a point on a surface, P a unit normal, a light source in the direction of the unit vector,, with a light intensity of I ambient light with an intensity, I a coefficients (rgb) of reflection of the surface: k a, k d, k s the shininess coefficient, n I p = k a *C a *I a + k d *C d * I * + k s * I *(V R) n I p = k a *C a *I a + I * ( k d *C d * + k s * (V R) n ) I p = k a *C*I a + I * ( k d * C* + k s * (V R) n ) if C=C a =C d Finding the R Vector Multiple ight Sources is derived from the object specification, is easily computed from the light s location and P But, how do we get R, the principal reflection direction? Project onto to get cosθ = Ν( ) From left triangle and vector arithmetic cosθ = + S So S = cosθ = ( ) Add another S from end of first S; it meets end of R From right triangle R = cosθ + S = ( )+( ) = 2( ) Can also derive from R = +S+S = + 2( ) 2 S S cosθ P R So far, we have only modeled 1 (point) light source Easy to add more I p = k a *I a + I * ( k d * + k s * (V R) n ) If we want each light to contribute to the ambient component, just add in k a * Ia 19 20

6 Blinn-Phong Specular Reflection ight Attenuation Blinn developed an alternative specular reflection model Instead of (R V) n, use ( H) n where H is the vector half way between and V if H is also a unit vector, H = cos β α and β are different angles, but are very similar as V approaches R How do we get H? Easier than R! H = (+V)/ +V β θ θ α Η R V In the real world, light diminishes with distance related to the distance squared from light to object need large distances to matter Can simulate a more flexible attenuation by defining an attenuation factor for each light:! 1 f = min c 1 + c 2 d + c 3 d, 1 \$ # 2 & " % where c 1, c 2, and c 3 are defined by user c 1 keeps the denominator from getting too small for small distances, and the other two constants allow some tuning, usually based on the relative distances of the objects with each other and the light source What about Color? Polygon Mesh Shading Visible light is an energy distribution from 400nm to 700nm Our visual system integrates the spectral energy distribution into a perception of color ighting model would be most correct if all light terms were expressed as functions of wavelength, λ I p (λ) = k a (λ)*i a (λ) + f * I (λ)* ( k d (λ)* + k s (λ)* (V R) n ) and evaluated for many different λ values (8-10 or more). For most purposes, 3 λ values are sufficient and computationally tractable. Usually these are values representing red, green, blue, so we have to compute 3 equations of the form above. ots of objects can be efficiently and effectively modeled as a mesh of polygons (triangles, usually) Shading options flat shading Gouraud color interpolation Phong normal interpolation 23 24

7 Flat Shading Get normal to plane of the polygon comes from polygon vertices if it is a triangle, the polygon is guaranteed to be planar if it has more than 3 vertices, there is a simple algorithm that will compute the plane normal if the vertices are coplanar, or the least error approximating plane Apply lighting model to get a color is usually computed as a vector from a point near the center of the polygon Color the entire polygon with that color Polygon Vertex Calculation Both Gouraud and Phong shading require normals to polygon vertices If mesh is generated from an underlying surface specification, get normals from the surface spec If all you have is the mesh, compute vertex normals by averaging polygon normals that share the vertex V Gouraud Mesh Shading Phong Mesh Shading Ia Id Ileft Ip Iright Ic Ib Intensity interpolation Use the vertex normals to compute intensities at each vertex I a, I b, I c, and I d Interpolate intensity along edges get I left from I a and I b.and I right from I c and I d Interpolate intensities between edges across scanline get I p from I left and I right. ormal interpolation Interpolate normals along edges Interpolate normals across scanline Apply shading model at each pixel. l b a p d Ip c r 27 28

8 Comparing Mesh Shading 1. Gouraud interpolation: shading model applied once/vertex 2. Phong interpolation: shading model applied once/pixel 3. Interpolation costs are the same: 3 colors or 3 component vector 4. Phong handles specular highlights more accurately 5. Gouraud is done in all graphics cards Generic Problems General problems with interpolatory shading polygon silhouette: curved surface silhouettes still show polygonal approximation perspective distortion: linear interpolation done in perspective world; not accurate in real world orientation dependence: interpolation is dependent on orientation shared vertices; get discontinuities if 2 adjacent polygons don't share vertex lying on shared edge. unrepresentative vertex normals: zigzag polygons can produce inaccurate vertices; appears flat 29 30

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