Ligh%ng in OpenGL. The Phong Illumina%on Model. Vector Background

Transcription

1 Ligh%ng in OpenGL The Phong Illumina%on Model Vector Background 1

2 Vector Dot Product The dot product of two vectors is a number:! x $ # 1 v 1 = # y 1 # " z 1 %! x $ # 2 v 2 = # y 2 # " z 2 % In GLSL you have dot(v1, v2)! v 1 v2 = x1 x 2 + y 1 y 2 + z 1 z 2 In GLM you have glm::dot(v1, v2)! If θ is the angle between the two vectors, then v2 = v1 v 1 v 2 cosθ The cross product of two vectors is a vector:! x $! 1 x $ # # 2 v 2 v 1 = # y 1 v 2 = # y 2 # " z 1 # % z 2 v " % 1 # y 1 z 2 z 1 y % 2 ( v 1 v2 v 1 v2 = % z 1 x 2 x 1 z 2 ( % x In GLSL you have 1 y 2 y 1 x 2 ( cross(v1, v2)! $ ' In GLM you have glm::cross(v1, v2)! Vector Cross Product If θ is the angle between the two vectors, then v 1 v2 = n v1 v 2 sinθ n is the unit vector perpendicular on v 1 and v 2 2

3 n Normal vectors p 2 n = p 1 p 0 p2 p 0 p 0 p p 1 n = n n The normal determines the outer face Note that the order of ver@ces is important Ligh%ng 3

4 Is this a plate or a ball? Without light, images look flat A lit sphere is a circular shape with many shades of color What color should we set for each pixel? Physical Reality As light hits the surface: part is absorbed part is reflected Law of reflec@on angle of incidence = angle of reflec@on true for smooth objects (glass, water) this is specular reflec+on Light may scaler in all direc@ons true for rough surfaces this is diffuse reflec+on Visible light includes all colors of the rainbow 4

5 Light Intensi%es Colors are of different of red, green and blue light. This is why the color of a light is called the intensity of the light Color Absorp%on and Reflec%on Physically, objects can be said to have the color of the light leaving their surfaces: 5

6 Color Absorp%on and Reflec%on If a blue object is illuminated with red light, it will appear If a magenta (red+blue) object is illuminated with cyan (green +blue) light, it will appear Calcula@ng the reflected color is simple (use dot product): light intensity * surface color = reflected color Example: cyan! magenta blue! (0, 1, 1) * (1,0,1) = (0,0,1)! Phong Illumina%on Model 6

7 Phong Illumina%on Model Method of the color of a pixel, based on surface and light source parameters Light source parameters include posi@on/direc@on of the light color/intensity of the light Surface parameters include color of the surface the direc@on the surface is facing (a.k.a the normal) "shininess" of the surface Phong Reflec%on Model Includes three components: Diffuse reflec@on Specular reflec@on Ambient light The total reflected light from a surface is the sum of the diffuse, specular and ambient components 7

8 Diffuse Reflec%on Light scalers with equal intensity in all Happens when the surface is rough N If surface has brightness Ι when facing light, it has brightness I*cos(θ) at angle θ. You will see the brightness wrilen as I(N L) L θ N L = cosθ (N, L are unit vectors) Diffuse Reflec%on A parameter k d set for each surface determines the frac@on of incident light scalered as diffuse reflec@ons from that surface. This parameter is known as the diffuse reflec@on coefficient or the diffuse reflec@vity I d = k d I(N L) k d = 0 k d = 0.25 k d = 0.5 k d = 0.75 k d =1 k d is assigned a value between 0.0 and for dull surface that absorbs almost all light 1.0 for shiny surface that reflects almost all light 8

9 Diffuse Reflec%on Summary I d k = d I( N L) 0 if if N L > 0 N L 0 Implemen@ng diffuse reflec@on in world space: uniform struct Light {! vec3 position; /* world space */! vec3 intensities;! } light;!! in vec3 fragnormal; /* object space */! in vec3 fragvert; /* object space */! // Calculate normal in world coordinates! vec3 N =...!! vec3 surfacepos = vec3(model * vec4(fragvert, 1)); /* world space */! vec3 L = normalize(light.position - surfacepos);!! float diffusecoeff = max(0, dot(n, L));! vec3 diffusecolor = diffusecoeff * light.intensities * fragcolor.rgb;!! Hands- on Session Run the lightmaterial tutor Make the light source diffuse- only Check the color of a blue object illuminated with red light Try different color combina@ons of diffuse light and material Change the light posi@on and observe the changes in color Combine diffuse and ambient light 9

10 Hands- On Ac%vity 1 Open the project 06_diffuse_lighting from opengl_series! Study the ligh@ng calcula@ons in the fragment shader Note that all calcula@ons are done in world space Study the way the fragment shader receives its ligh@ng parameters: fragnormal and fragvert these are values passed by the vertex shader through the interpola@on stage to the fragment shader. They are given in model space, so the fragment shader must bring them to world space before processing light this is a uniform variable containing the posi@on (in world space) and the intensi@es/color of the light, passed directly by the applica@on to the fragment shader Hands- On Ac%vity 2 Add code to the Update func@on to make the camera rotate around the scene. You can accomplish this by sebng the camera posi@on to dependent value (radius*cos(+me), 0, radius*sin(+me)), so that it moves in a circle. Note how the ligh@ng is different on different parts of the scene. Try to explain these differences using Phong's ligh@ng model. 10

11 Hands- On Ac%vity 3 In the previous ac@vity you no@ced that the scene looked dark from the sides and the back. This is because the light has a fixed posi@on in front of the scene and no light rays hit the sides and the back of the scene (N L < 0 and therefore the diffuse intensi@es are all 0). Add code to the Update func@on to alach the light source to the camera so that the light source moves with the camera. No@ce the changes in ligh@ng. 11