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# CG OpenGL Shadows + Light + Texture -course 10

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Introduce the relationship between light and shadow...

How to create a texture

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### CG OpenGL Shadows + Light + Texture -course 10

1. 1. Shadows + Light +Texture Chen Jing-Fung (2006/12/15) Assistant Research Fellow, Digital Media Center, National Taiwan Normal UniversityCh10: Computer Graphics with OpenGL 3th, Hearn BakerCh6: Interactive Computer Graphics 3th, Addison WesleyCh7: Interactive Computer Graphics 3th, Addison Wesley
2. 2. outline• How to construct the object’s shadow in a scene• Camera’s walking in a scene• Several kinds about light 2
3. 3. shadows• Create simple shadows is an interesting application of projection matrices – Shadows are not geometric objects in OpenGL – Shadows can realistic images and give many visual clues to the spatial relationships among objects in a scene 3
4. 4. How to create the object’s shadow• Starting from a view point• Lighting source is also required (infinitely light) – If light source is at the center of projection, there are no visible shadows (shadows are behind the objects) 4
5. 5. Polygon’s shadow y• Consider the shadow (xl,yl,zl) generated by the point source – Assume the shadow falls on the surface (y=0) x – Then, the shadow polygon is z related to original polygon • Shadow ~ origin 5
6. 6. y (xl,yl,zl) z x• Find a suitable projection matrix and use OpenGL to compute the vertices of the shadow polygon is projected to – (x,y,z) in space -> (xp, yp, zp) in projection plane – Characteristic: • All projectors pass through the origin and all projected polygon through the vertical to y-axis 6
7. 7. y (xl,yl,zl)z x • Shadow point and polygon point are projected from x-axis to y-axis x (xp,-d) (x,y) xp x x  xp  d y y / d y yp = -d • Project from z-axis to y-axis (zp,-d) z (z,y) zp z z  zp  d y y / d y y = -d p 7
8. 8. Homogeneous coordinates• Original homogeneous coordinates: x  x p  1 0 0 0  x  xp  y / d  y  0 1 0 0  y   p     yp = y  zp  0 0 1 0  z  zp  z   0 1  0 0  1  y / d 1   d   Perspective projection matrix: Our light can be shadow projection Matrix moved by design GLfloat light[3]={0.0, 10.0, 0.0}; GLfloat m[16]; light[0]=10.0*sin((6.28/180.0)*theta); light[2]=10.0*cos((6.28/180.0)*theta); for(i=0;i<16;i++) m[i]=0.0; m[0]=m[5]=m[10]=1.0; m[7]=-1.0/light[1]; 8
9. 9. Orthogonal view with clipping box glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);/* set up standard orthogonal view with clipping *//* box as cube of side 2 centered at origin */ glMatrixMode (GL_PROJECTION); glLoadIdentity (); glOrtho(-2.0, 2.0, -2.0, 2.0, -5.0, 5.0); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); gluLookAt(1.0,1.0,1.0,0.0,0.0,0.0,0.0,1.0,0.0); // view plane up vector at y-axis (0.0,1.0,0.0) 9
10. 10. Polygon & its shadow /* define unit square polygon */ glColor3f(1.0, 0.0, 0.0);/* set drawing/fill color to red*/ glBegin(GL_POLYGON); glVertex3f(…); … glEnd(); glPushMatrix(); //save state glTranslatef(light[0], light[1],light[2]); //translate back glMultMatrixf(m); //project glTranslatef(-light[0], -light[1],-light[2]); //return origin //shadow object glColor3f(0.0,0.0,0.0); glBegin(GL_POLYGON); glVertex3f(…);… glEnd(); glPopMatrix(); //restore state How to design the different size between original polygon & its shadow? 10
11. 11. Special key parametervoid SpecialKeys(int key, int x, int y){ if(key == GLUT_KEY_UP){ theta += 2.0; if( theta > 360.0 ) theta -= 360.0; //set range’s boundary } if(key == GLUT_KEY_DOWN){ theta -= 2.0; y if( theta < 360.0 ) theta+= 360.0; } glutPostRedisplay(); } demo z x 11
12. 12. How to design walking object?• Walking direction?• Viewer (camera) parameter• Reshape projected function 12
13. 13. Viewer (camera) moving (1)• Viewer move the camera in a scene by depressing the x, X, y, Y, z, Z keys on keyboard void keys(unsigned char key, int x, int y){ if(key == ‘x’) viewer[0] -= 1.0; if(key == ‘X’) viewer[0] += 1.0; if(key == ‘y’) viewer[1] -= 1.0; if(key == ‘Y’) viewer[1] += 1.0; if(key == ‘z’) viewer[2] -= 1.0; if(key == ‘Z’) viewer[2] += 1.0; glutPostRedisplay(); } Walking in a scene. What problem happen if object is walked far away? 13
14. 14. Viewer (camera) moving (2)• The gluLookAt function provides a simple way to reposition and reorient the camera void display(void){ glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); glLoadIdentity(); gluLookAt(viewer[0],viewer[1],viewer[2],0.0,0.0,0.0,0.0,1.0,0.0); /* rotate cube */ glRotatef(theta[0], 1.0, 0.0, 0.0); glRotatef(theta[1], 0.0, 1.0, 0.0); glRotatef(theta[2], 0.0, 0.0, 1.0); colorcube(); glFlush(); glutSwapBuffers(); } 14
15. 15. Viewer (camera) moving (3)• Invoke glFrustum in the reshape callback to specify the camera lens void myReshape(int w, int h){ glViewport(0, 0, w, h); glMatrixMode(GL_PROJECTION); glLoadIdentity(); if(w<=h) glFrustum(-2.0, 2.0, -2.0 * (GLfloat) h/ (GLfloat) w, 2.0* (GLfloat) h / (GLfloat) w, 2.0, 20.0); else glFrustum(-2.0, 2.0, -2.0 * (GLfloat) w/ (GLfloat) h, 2.0* (GLfloat) w / (GLfloat) h, 2.0, 20.0); glMatrixMode(GL_MODELVIEW); } demo 15
16. 16. Light & surface• Light reflection method is very complicated – Describe that light source is reflected from an actual surface – Maybe depends an many factors • Light source’s direction, observer’s eye and the normal to the surface – Surface characteristics can also consider that its roughness or surface’s color … (surface’s texture) 16
17. 17. Why do shading?• Set a sphere model to cyan – Result • the sphere seem like a circle• We want to see a sphere – Material + light + viewer + surface orientation • The material’s color can be designed to a gradual transformation 17
18. 18. Lighting phenomenon• Light sources – Point light sources • Infinitely distant light sources • Radial intensity attenuation – Directional light sources and spotlight effects • Angular intensity attenuation• Surface lighting effects 18
19. 19. Point light sources• The simplest model for an object and its light source – Light rays are generated along radially diverging paths from the single-color source position • light source is a single color – The light source’s size is smaller than object – We can use an illumination model to calculate the light direction to a selected object surface’s position 19
20. 20. Infinitely distant light sources• A large light source (sun) that is very far from a scene like a point light source• Large light source is small different to point light source – When remote the point light source, the object is illuminated at only one direction – In constant to sun which is very far so it shines everywhere 20
21. 21. Radial intensity attenuation (1)• As radiant energy from a light source travels outwards through space, its amplitude at any distance dl from the source is decreased by the factor 1/dl2 d ’ l Energy =1 light Energylight = 1/dl’ 2 dl Energylight = 1/dl2 21
22. 22. Radial intensity attenuation (2) • General form to the object about the infinity light source and point light source  1.0 if source is at infinity fl ,radatten  1  a0  a1d l  a2d l  2 if source is local 22
23. 23. Directional light sources and spotlight effects• A local light source can easily be modified to produce a directional, or spotlight, beam of light. – The unit light-direction vector defines the axis of a light cone, the angle θl defines the angular extent of the circular cone Vlight Light direction vector Light source θl 23
24. 24. spotlight effects• Denote Vlight in the light-source direction and Vobj in the direction from the light position to an object position To object Vobj vertex α Cone axis Vlight vector if Vobj .Vlight < cosθl -> Light Vobj .Vlight = cos α the object is outside source the light cone cos α >= cosθl θl 00 <θl<= 900 24
25. 25. Angular intensity attenuation• For a directional light source, we can degrade the light intensity angularly about the source as well as radially out from the point-source position. – Light intensity decreasing as we move farther from the cone axis – Common angular intensity-attenuation function for a directional light source f angatten( )  cos al  0     25
26. 26. Attenuation function f angatten( )  cos al  0    – al (attentuation exponent) is assigned positive value • (al: the greater value in this function)– Angle φis measured from the cone axis • Along the cone axis, φ=0o fangatten(φ)=1.0 26
27. 27. Combination above different light sources• To determine the angular attenuation factor along a line from the light position to a surface position in a scene  1.0 if source is not a spotlight  f l ,radatten   0.0 if Vobj .Vlight = cos α < cosθl (V  V ) al  obj light otherwise 27
28. 28. Surface lighting effects• Besides light source can light to object, object also can reflect lights – Surfaces that are rough so tend to scatter the reflected light • when object exist more faces of surface, more directions can be directed by the reflected light 28
29. 29. Specular reflection• Some of the reflected light is concentrated into a highlight called specular reflection – The lighting effect is more outstanding on shiny surfaces 29
30. 30. Summary light & surface• Surface lighting effects are produced by a combination of illumination from light sources and reflections from other surfaces Surface is not directly exposed to a light source may still be visible due to the reflected light from nearby objects. The ambient light is the illumination effect produced by the reflected light from various surfaces 30
31. 31. Homework• Walking in a scene void polygon(int a, int b, int c , int d){ – Hint: Object glBegin(GL_POLYGON); walking or walking glColor3fv(colors[a]); glNormal3fv(normals[a]); above floor glVertex3fv(vertices[a]); glColor3fv(colors[b]); – Example: color glNormal3fv(normals[b]); cube glVertex3fv(vertices[b]); glColor3fv(colors[c]); glNormal3fv(normals[c]); glVertex3fv(vertices[c]); glColor3fv(colors[d]); glNormal3fv(normals[d]); glVertex3fv(vertices[d]); glEnd(); } demo 31
32. 32. TextureCh10: Computer Graphics with OpenGL 3th, Hearn BakerCh7: Interactive Computer Graphics 3th, Addison Wesley
33. 33. Mapping methods• Texture mapping• Environmental maps• The complex domain’s figure 33
34. 34. Simple buffer mapping• How we design program which can both write into and read from buffers. • (Generally, two factors make these operations different between reading and writing into computer memory) – First, read or write a single pixel or bit – Rather, extend to read and write rectangular blocks of pixels (called bit blocks) 34
35. 35. Example: read & write I love monitor OpenGL• Our program would follow user controlling when user assign to fill polygon, user key some words or user clear the window• Therefore, both the hardware and software support a set of operations – The set of operations work on rectangular blocks of pixels • This procedure is called bit-block transfer • These operations are raster operations (raster-ops) 35
36. 36. bit-block transfer (bitblt)• Take an n*m block from the source buffer and to copy it into another buffer (destination buffer) Write_block(source,n,m,x,y,destination,u,v);• source and destination are the buffer• the n*m source block which lower-left corner is at (x,y) to the destination destination buffer at a location (u,v)• the bitblt is that a single function call alters the destination block source n Frame buffer m 36
37. 37. raster operations (raster-ops)• The mode is the exclusive OR or XOR mode True table ’ d=d⊕s s d d’ Source pixel (s) 0 0 0 XOR Destination pixel (d’) 0 1 1 Read pixel (d) Color 1 0 1 buffer 1 1 0 glEnable(GL_COLOR_LOGIC_OP) glLogicOp(GL_XOR) 37
38. 38. Erasable Line• What is Erasable Line ?• How to implement? 38
39. 39. Drawing erasable lines• Why line can erasable – Line color and background color are combined togrther• How to do – First, we use the mouse to get the first endpoint and store it. xm=x/500.; ym=(500-y)/500.; – Then, get the second point and draw a line segment in XOR mode xmm = x/500.; ymm=(500-y)/500.; glColor3f(1.0,0.0,0.0); glLogicOp(GL_XOR); glBegin(GL_LINES); glVertex2f(xm,ym); glVertex2f(xmm,ymm); glEnd(); glLogicOp(GL_COPY); glFlush(); 39
40. 40. Texture mapping • Texture mapping which describe a pattern map to a surface • describe texture: parametric compute textures Regular pattern 40Ch7: Interactive Computer Graphics 3th, Addison Wesley
41. 41. Texture elements• Texture elements which can be put in a array T(s,t) – This array is used to show a continuous rectangular 2D texture pattern – Texture coordinates (s, t) which are independent variables • With no loss of generality, scale (s, t) to the interval (0, 1) 41
42. 42. Texture maps (1)• Texture map on a geometric object where mapped to screen coordinates for display – Object in spatial coordinates [(x,y,z) or (x,y,z,w)] & texture elements (s,t) • The mapping function: x = x(s,t), y = y(s,t), z = z(s,t), w = w(s,t) • The inverse function: s = s(x,y,z,w), t = t(x,y,z,w) 42
43. 43. Texture maps (2)• If the geometric object in (u,v) surface (Ex: sphere…) – Object’s coordination (x,y,z) - > (u,v) – Parametric coordinates (u,v) can also be mapped to texture coordinates – Consider the projection process from worldcoordination to screencoordination • xs = xs(s,t), ys = ys(s,t) 43
44. 44. Texture maps (3) First, determine the map from texture coordinate to geometric coordinates. The mapping from this rectangle to Third, we can use an arbitrary region in 3D space the texture maps to vary the object’s Second, owing to the nature of shape the rendering process, which works on a pixel-by-pixel 44Ch7: Interactive Computer Graphics 3th, Addison Wesley
45. 45. Linear mapping function (1)• 2D coordinated map t xs (rmax,smax) (umax,vmax) (umin,vmin) (rmin,smin) s ys s  smin u  umin  (umax  umin ) smax  smin t  t min v  vmin  (vmax  vmin ) t max  t min 45
46. 46. Linear mapping function (2) • Cylinder coordination t s u and v ~ (0,1) x  r cos(2u ) => s = u, t = v y  r sin( 2v) z  v/h 46
47. 47. Linear mapping function (3)• Texture mapping with a box t Back Left Bottom Right Top s Front 47
48. 48. Pixel and geometric pipelines • OpenGL’s texture maps rely on its pipeline architecturevertices Geometric rasterization display processing pixels Pixel operations 48
49. 49. Texture mapping in OpenGL (1)• OpenGL contained the functionality to map 1D and 2D texture to one- through 4D graphical objects• The key issue on texture mapping – The pixel pipeline can be mapped onto geometric primitives. vertices Geometric processing pixels Pixel operations 49
50. 50. Texture mapping in OpenGL (2)• In particular, texture mapping is done as primitives are rasterized• This process maps 3D points to locations (pixels) on the display• Each fragment that is generated is tested for visibility (with z-buffer) 50
51. 51. 2D texture mapping (1)• Support we have a 512*512 image my_texels GLubye my_texels[512][512]• Specify this array is too be used as a 2D texture glTexImage2D(GL_TEXTURE_2D, level, components, width, height, border, format,type,tarry); – tarray size is the same the width*height – The value components is the (1-4) of color components (RGBA) or 3 (RGB) – The format (RGBA) = 4 or 3 (RGB) – In processor memory, tarry’s pixels are moved through the pixel pipeline (** not in the frame buffer) – The parameters level and border give us fine control Ex: glTexImage2D(GL_TEXTURE_2D, 0, 3, 512, 512, 0, GL_RGB,GL_UNSIGNED_BYTE,my_texels); 51
52. 52. 2D texture mapping (2)• Enable texture mapping glEnable(GL_TEXTURE_2D);• Specify how the texture is mapped onto a geometric object t (512,512) 1 1 s (0,0) glTexCoord2f(s,t); glVertex2f(x,y,z); glBegin(GL_QUAD); glTexCoord2f(0.0,0.0); glVertex2f(x1,y1,z1); …. glEnd(); 52
53. 53. 2D texture mapping (3)t • Mapping texels to pixels t xs xs s ys s ys Magnification: large Minification: min glTexParameteri(GL_TEXTURE_2D,GL_TEXTURE_MAG_FILTER, GL_NEAREST); glTexParameteri(GL_TEXTURE_2D,GL_TEXTURE_MIN_FILTER, GL_NEAREST); 53
54. 54. Texture objects • Texture generation in frame bufferFragment Texture unit 0 Texture unit 1 Frame buffer Texture unit 2 54
55. 55. Environmental maps• Mapping of the environment Object in environment Projected object T(s,t) Intermediate surface glTexGeni(GL_S,GL_TEXTURE_GEN_MODE,GL_SPHERE_MAP); glTexGeni(GL_T,GL_TEXTURE_GEN_MODE,GL_SPHERE_MAP); glEnable(GL_TEXTURE_GEN_S); glEnable(GL_TEXTURE_GEN_T); 55
56. 56. The complex domain’s figure• The mandelbrot set z1=x1+iy1 z1+z2=(x1+x2)+i(y1+y2) z2=x2+iy2 z1z2 = x1x2-y1y2+i(x1y2+x2y1) A complex recurrence |z|2=x2+y2 y zk+1=F(zk) y Attractors: zk+1=zk2 z =x + iy z3=F(z2) z2=F(z1) x x z0 z1=F(z0) Complex plane Paths from complex recurrence The complex plane’s Attractors general: function w=F(z) zk+1=zk2+c 56
57. 57. Pixels & display The area centered at -0.75+i0.0 If |zk|>4, break 0~255 -> Rarray demo 57