CGT520 Lighting. Lighting. T-vertices. Normal vector. Color of an object can be specified 1) Explicitly as a color buffer

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1 CGT520 Lighting Lighting Color of an object can be specified 1) Explicitly as a color buffer Bedrich Benes, Ph.D. Purdue University Department of Computer Graphics 2) Implicitly from the illumination model. Color is then a result of interaction of lights and material properties. T-vertices The T-vertex and lighting T-vertex causes illumination artifacts Normal vector Normal vectors are essential for correct lighting calculation They provide direction of the surface Used to calculate reflected rays It must be provided by the application It is usually bound to VBO Wikipedia

2 Normal vector Normal vectors provided by the application. Usually a part of the model Analytic surfaces: given by the partial derivation of the two main tangent directions Triangular meshes: can be approximated for Analytic Surfaces Having a surface The tangents in the principal directions are: The normal vector is Wikipedia for triangles Use local differences and the vector product C for triangular meshes Its is better, for smooth appearance, to calculate normals per vertex Corners are treated as 0 vectors A B

3 for triangular meshes a) normals per face b) normals per vertex (average of the a) ) for triangular meshes Another way Take the cross of the four neighbors and calculate its vector product denote distance in, between the points height of right, left, up, and down for triangular meshes After doing some simple calculations: Normal Vector Transformation Problem: must be normalized

4 Normal Vector Transformation Let transform an object to eye space Normal vectors must be transformed by: Where is transpose of the inverse of the upper matrix of also called contravariant tensor of rank 1 Normal Vector Transformation Normal vector represent a tangent plane or simply Normal Vector Transformation If we transform both is the standard vertex transformation is transform of the normal, but we need to multiply from the left is the normal transform Normal Vector Transformation GLM implementation //modeling transform for vertices glm::mat4 modelv; //modeling transform for normals glm::mat3 modeln=glm::mat3(modelv); modeln= glm::transpose(glm::inverse(modeln));

5 Normal Vector Normals are stored in the VBO Vertex Array can hold multiple data sets in multiple Vertex Buffer Objects During rendering, all that is enabled is sent to the GPU VBO for vertices and normals points=vertex.size();normals=normal.size(); //get the vertex array handle and bind it glgenvertexarrays(1,&vaid); glbindvertexarray(vaid); //generate the VBOs vertices and normals glgenbuffers(2, vbohandles); GLuint verticesid=vbohandles[0]; GLuint normalsid =vbohandles[1]; VBO for vertices and normals //send vertices glbindbuffer(gl_array_buffer, verticesid); glbufferdata(gl_array_buffer, points*sizeof(glfloat), &vertex[0],gl_static_draw); glvertexattribpointer((gluint)0, 3, GL_FLOAT,GL_FALSE,0,0); glenablevertexattribarray(0); VBO for vertices and normals //send normals glbindbuffer(gl_array_buffer, normalsid); glbufferdata(gl_array_buffer, normals*sizeof(glfloat), &normal[0],gl_static_draw); glvertexattribpointer((gluint)1, 3, GL_FLOAT,GL_FALSE,0,0); glenablevertexattribarray(1);

6 GLSL Layout Qualifiers Let s have following shaders Vertex Array VBO 0 pos VBO 1 norm layout=0 ipos layout=1 inorm vs light, material model,view,projection layout=0 fs GLSL Layout Qualifiers We know vertices are assigned to VBO 0 normals are assigned to VBO 1 This is recognized in the shader by layout (location=0) in vec4 ipos; layout (location=1) in vec3 inorm; GLSL Layout Qualifiers We can also specify the output layout (location=0) out vec4 ocolor; Summary GPU holds two VBOs: vertices and normals Vertex Shader receives them Vertex Shader sends color on its output This is then used in the fragment shader layout (location=0) in vec4 icolor; What should be the color of the vertex?

7 Phong Illumination Model Bui Tuong Phong (1973) University of Utah Empirical model of light reflection. Light is ambient diffuse specular Material as well Ambient Light is constant in the entire scene Rough approximation of multiple reflections and scattering (intensity of ambient) Light Sources Characterized by their diffuse and specular component Material Material is characterized by its ability to reflect: specular light diffuse light ambient light shinniness

8 More is needed Direction to the camera (viewer) Direction to the light The normal vector The vertex position The light position Ambient term Ambient light does not have a position, Ambient Light Ambient light is everywhere, does not have direction, does not change vs for ambient vec4 Ra=vec4(0.2,0.2,0.2,1); ambient is set fix to some gray value

9 Diffuse Reflection Depends on the position of the light source and the vertex is the dot product is the normalized direction to the light Diffuse Reflection Lambertian or matte reflection incoming light is spread into all directions with equal probability an example is a plastic material or chalk perfect diffuse surface (Lambertian surface) f r = d / d is the ratio of the reflected to the incident energy (0 d 1) and cosd Diffuse Reflection Diffuse Reflection Diffuse light depends on the direction of the light and the normal vector changes with the cosine of the angle

10 vs for Diffuse - function vec4 Diffuse(vec3 n, vec4 pos, vec4 lightpos, vec3 ld, vec3 kd) { vec3 l=normalize(vec3(lightpos-pos)); vec3 col=kd*ld*max(0,dot(n,l)); return vec4(col,1); } vs for Diffuse - call layout (location=0) in vec4 iposition; layout (location=1) in vec3 inormal; layout (location=0) out vec4 ocolor; uniform mat4 model; uniform mat3 modelviewn; uniform mat4 view; uniform mat4 proj; vs for Diffuse - call void main() { //n to camera coords vec3 normal=normalize(modelviewn*inormal); //v to camera coordinates vec4 vert=view*model*iposition; ocolor=diffuse(normal,vert, lightpos,ld,kd); gl_position=proj*vert; } Specular Reflection Depends on the v, and the eye position v is vector to the viewer, is the reflected ray direction, and is the shininess coefficient is vector pointing to the light, is the normal vector to the surface

11 Specular Reflection Specular (glossy) reflection ~ acts as a ray of light ~ idealized specular surface is mirror Specular Reflection ~ Perfect specular surface (mirror) d ( m ) / cos s s is the ratio of the reflected to the incident energy (0 s 1) the Dirac pulse is 1 ( m) { 0 1 m otherwise Specular Reflection Specular light depends on the direction of the light, the normal vector, and the position of the viewer The shininess coefficient

12 Diffuse and Specular Combined Material definition Material GL AMBIENT GL DIFFUSE GL SPECULAR GL SHININESS Brass Bronze Polished Bronze Chrome Material definition Material GL AMBIENT GL DIFFUSE GL SPECULAR GL SHININESS Copper Polished Copper Gold Polished Gold Pewter vs for Specular and Diffuse layout (location=0) in vec4 iposition; layout (location=1) in vec3 inormal; layout (location=0) out vec4 ocolor; uniform mat4 model; uniform mat3 modelviewn; uniform mat4 view; uniform mat4 proj; uniform LightS light; uniform MaterialS mat;

13 vs for Specular and Diffuse struct LightS{ vec4 lpos; //position of the light vec3 la; //ambient, diffuse, specular vec3 ld; vec3 ls; }; struct MaterialS{ vec3 ka; vec3 kd; vec3 ks; float sh; }; vs for Specular - body void main() { //n to camera coords vec3 ncam=normalize(modelviewn*inormal); //v to camera coordinates vec4 vcam=view*model*iposition; ocolor=lighting(ncam,vcam,light,mat) gl_position=proj*vcam; } vs for Specular - function vec4 Lighting(vec3 n, vec4 pos, LightS light, MaterialS mat){ vec3 l=normalize(vec3(light.lpos-pos)); vec3 v=normalize(-pos.xyz); vec3 r=reflect(-l, n); float sdot=max(dot(l,n),0.0); vec3 diffuse=light.ld*mat.kd*sdot; vec3 specular=vec3(0.0); if (sdot>0)//just the front faces specular=light.ls*mat.ks* pow(max(dot(r,v),0.0),mat.sh); return vec4(diffuse+specular,1); Blinn-Phong Specular Term depends on is so called bisector, is the shininess coefficient No reflected vector is needed, so it is slightly faster But also a bit different V N H L }

14 Multiple Light Sources Reflected light is global ambient term plus sum of the diffuse and specular contributions of all lights Per Vertex Lighting Illumination is calculated per vertex constant interpolated high tessellation The result is clamped to [0,1] It means, if the reflection is 1 another light does not increase it! Per??? Lighting Color interpolation is also called Gouraud shading [guroood] Per fragment lighting Phong shading If we would interpolate the normal in the fragment shader and calculate the illumination per fragment, we would have Phong shading [fong] Wikipedia

15 Side note Phong shading means normal interpolation and then calculation illumination Phong lighting means using the illumination model (ADS ambient, diffuse, specular) Per Fragment Lighting the lighting function is the same the difference is that we calculate it per fragment rather than per vertex how? we need to interpolate the normal vector it is a collaboration of vs and fs Comparison Normal Interpolation per vertex 15x15 per fragment 5x5 VS will send vertex and normal coordinates in the camera space GPU will interpolate them FS will calculate the illumination important thing! the normal vector must be renormalized! because result of an interpolation is not (in general) normalized

16 vs and fs communication Compare to per vertex Vertex Array VBO 0 pos VBO 1 norm layout=0 ipos layout=1 inorm vs model,view,projection layout=0 iposcamera layout=1 inormcamera light, material fs Vertex Array VBO 0 pos VBO 1 norm layout=0 ipos layout=1 inorm vs light, material model,view,projection layout=0 fs the vs for per fragment lighting layout (location=0) in vec4 iposition; layout (location=1) in vec3 inormal; layout (location=0) out vec4 oposcam; layout (location=1) out vec3 onormalcam; uniform mat4 model; uniform mat3 modelviewn; uniform mat4 view; uniform mat4 proj; the vs for per fragment lighting void main() { //n to camera coords onormalcam=normalize(modelviewn*inormal); //v to camera coords oposcam=view*model*iposition; //standard vertex out gl_position = proj*oposcam; }

17 the fp for per fragment lighting layout (location=0) in vec4 iposcamera; layout (location=1) in vec3 inormcamera; layout (location=0) out vec4 ocolor; uniform MaterialS mat; uniform LightS light; Compare void main() { ocolor=lighting(normalize(inormcamera), iposcamera,light,mat); } //the Lighting function is the same per fragment per vertex Reading GLSL Specification ngspec clean.pdf Reading Edward Engel Interactive Computer Graphics: A Top-Down Approach with Shader-Based OpenGL (6th Edition) Chapters 3 and 4 OpenGL Mathematics (GLM) David Wolff, OpenGL 4.0 Shading Language Cookbook, PACKT Publishing 2011