[SOLVED] CS data structure 15-462 Computer Graphics I Lecture 8

15-462 Computer Graphics I Lecture 8
Shading in OpenGL
Shading in OpenGL
Polygonal Shading
Polygonal Shading
Light Source in OpenGL
Light Source in OpenGL
Material Properties in OpenGL
Material Properties in OpenGL
Normal Vectors in OpenGL
Normal Vectors in OpenGL
Approximating a Sphere
Approximating a Sphere
[Angel 6.5-6.9]
[Angel 6.5-6.9]
February 6, 2003
Frank Pfenning
Carnegie Mellon University
http://www.cs.cmu.edu/~fp/courses/graphics/

Polygonal Shading
Polygonal Shading
Curved surfaces are approximated by polygons
How do we shade? Flat shading
Interpolative shading Gouraud shading
Phong shading (different from Phong illumination)
Two questions:
How do we determine normals at vertices?
How do we calculate shading at interior points?
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Flat Shading
Flat Shading
Normal: given explicitly before vertex
glNormal3f(nx, ny, nz); glVertex3f(x, y, z);
Shading constant across polygon
Single polygon: first vertex
Triangle strip:Vertex n+2 for triangle n
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Flat Shading Assessment
Flat Shading Assessment
Inexpensivetocompute
Appropriateforobjectswithflatfaces Lesspleasantforsmoothsurfaces
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Interpolative Shading
Interpolative Shading
Enable with glShadeModel(GL_SMOOTH);
Calculatecolorateachvertex
Interpolatecolorininterior
Compute during scan conversion (rasterization) Much better image (see Assignment 1)
Moreexpensivetocalculate
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Gouraud Shading
Gouraud Shading
Specialcaseofinterpolativeshading
How do we calculate vertex normals?
Gouraud:averagealladjacentfacenormals
Requires knowledge about which faces share a vertex
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Data Structures for Gouraud Shading
Data Structures for Gouraud Shading
Sometimesvertexnormalscanbecomputed directly (e.g. height field with uniform mesh)
More generally, need data structure for mesh Key: which polygons meet at each vertex
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Phong Shading
Phong Shading
Interpolatenormalsratherthancolors
Significantly more expensive
Mostlydoneoff-line(notsupportedinOpenGL)
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Phong Shading Results
Phong Shading Results
Michael Gold, Nvidia
Single pass Phong Lighting Gouraud Shading
02/06/2003
Two pass Phong Lighting, Gouraud Shading
15-462 Graphics I
Two pass Phong Lighting, Phong Shading
9

Polygonal Shading Summary
Polygonal Shading Summary
Gouraud shading Set vertex normals
Calculate colors at vertices
Interpolate colors across polygon
Must calculate vertex normals!
Must normalize vertex normals to unit length!
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Outline
Outline
Polygonal Shading
Light Sources in OpenGL
MaterialPropertiesinOpenGL
NormalVectorsinOpenGL
Example: Approximating a Sphere
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Enabling Lighting and Lights
Enabling Lighting and Lights
Lighting in general must be enabled
glEnable(GL_LIGHTING);
Each individual light must be enabled
glEnable(GL_LIGHT0);
OpenGLsupportsatleast8lightsources
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Global Ambient Light
Global Ambient Light
Setambientintensityforentirescene
GLfloat al[] = {0.2, 0.2, 0.2, 1.0}; glLightModelfv(GL_LIGHT_MODEL_AMBIENT, al);
The above is default
Also: local vs infinite viewer
glLightModeli(GL_LIGHT_MODEL_LOCAL_VIEWER, GL_TRUE);
Moreexpensive,butsometimesmoreaccurate 02/06/2003 15-462 Graphics I 13

Defining a Light Source
Defining a Light Source
Usevectors{r,g,b,a}forlightproperties Beware: light source will be transformed!
GLfloat light_ambient[] = {0.2, 0.2, 0.2, 1.0};
GLfloat light_diffuse[] = {1.0, 1.0, 1.0, 1.0};
GLfloat light_specular[] = {1.0, 1.0, 1.0, 1.0};
GLfloat light_position[] = {-1.0, 1.0, -1.0, 0.0}; glLightfv(GL_LIGHT0, GL_AMBIENT, light_ambient); glLightfv(GL_LIGHT0, GL_DIFFUSE, light_diffuse); glLightfv(GL_LIGHT0, GL_SPECULAR, light_specular); glLightfv(GL_LIGHT0, GL_POSITION, light_position);
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Point Source vs Directional Source
Point Source vs Directional Source
Directional light given by position vector GLfloat light_position[] = {-1.0, 1.0, -1.0, 0.0};
glLightfv(GL_LIGHT0, GL_POSITION, light_position); Point source given by position point
GLfloat light_position[] = {-1.0, 1.0, -1.0, 1.0}; glLightfv(GL_LIGHT0, GL_POSITION, light_position);
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Spotlights
Spotlights
Create point source as before
Specifyadditionalpropertiestocreatespotlight
GLfloat sd[] = {-1.0, -1.0, 0.0}; glLightfv(GL_LIGHT0, GL_SPOT_DIRECTION, sd); glLightf(GL_LIGHT0, GL_SPOT_CUTOFF, 45.0); glLightf(GL_LIGHT0, GL_SPOT_EXPONENT, 2.0);
[Demo: Lighting Position Tutor]
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Outline
Outline
Polygonal Shading
Light Sources in OpenGL
MaterialPropertiesinOpenGL
NormalVectorsinOpenGL
Example: Approximating a Sphere
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Defining Material Properties
Defining Material Properties
Materialpropertiesstayineffect
Setbothspecularcoefficientsandshininess
GLfloat mat_d[] = {0.1, 0.5, 0.8, 1.0};
GLfloat mat_s[] = {1.0, 1.0, 1.0, 1.0};
GLfloat low_sh[] = {5.0};
glMaterialfv(GL_FRONT, GL_AMBIENT, mat_d); glMaterialfv(GL_FRONT, GL_SPECULAR, mat_s); glMaterialfv(GL_FRONT, GL_SHININESS, low_sh);
Diffusecomponentisanalogous
[Demo: Light material Tutor]
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Color Material Mode (Answer)
Color Material Mode (Answer)
CanshortcutmaterialpropertiesusingglColor Must be explicitly enabled and disabled
glEnable(GL_COLOR_MATERIAL);
/* affect front face, diffuse reflection properties */ glColorMaterial(GL_FRONT, GL_DIFFUSE); glColor3f(0.0, 0.0, 0.8);
/* draw some objects here in blue */ glColor3f(1.0, 0.0, 0.0);
/* draw some objects here in red */ glDisable(GL_COLOR_MATERIAL);
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Outline
Outline
Polygonal Shading
Light Sources in OpenGL
MaterialPropertiesinOpenGL
NormalVectorsinOpenGL
Example: Approximating a Sphere
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Defining and Maintaining Normals
Defining and Maintaining Normals
Defineunitnormalbeforeeachvertex glNormal3f(nx, ny, nz);
glVertex3f(x, y, z);
Lengthchangesundersometransformations
Ask OpenGL to re-normalize (all tfms)
glEnable(GL_NORMALIZE);
AskOpenGLtore-scalenormal glEnable(GL_RESCALE_NORMAL);
Works for uniform scaling (and rotate, translate) 02/06/2003 15-462 Graphics I 21

Example: Icosahedron
Example: Icosahedron
Define the vertices
#define X .525731112119133606 #define Z .850650808352039932
static GLfloat vdata[12][3] = {
{-X, 0.0, Z}, {X, 0.0, Z}, {-X, 0.0, -Z}, {X, 0.0, -Z}, {0.0, Z, X}, {0.0, Z, -X}, {0.0, -Z, X}, {0.0, -Z, -X}, {Z, X, 0.0}, {-Z, X, 0.0}, {Z, -X, 0.0}, {-Z, -X, 0.0}
};
For simplicity, avoid the use of vertex arrays
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Defining the Faces
Defining the Faces
Index into vertex data array
static GLuint tindices[20][3] = {
{1,4,0}, {4,9,0}, {4,9,5}, {8,5,4}, {1,8,4}, {1,10,8}, {10,3,8}, {8,3,5}, {3,2,5}, {3,7,2}, {3,10,7}, {10,6,7}, {6,11,7}, {6,0,11}, {6,1,0}, {10,1,6}, {11,0,9}, {2,11,9}, {5,2,9}, {11,2,7}
};
Becarefulaboutorientation!
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Drawing the Icosahedron
Drawing the Icosahedron
Normal vector calculation next
glBegin(GL_TRIANGLES); for (i = 0; i < 20; i++) {icoNormVec(i); glVertex3fv(&vdata[tindices[i][0]] [0]); glVertex3fv(&vdata[tindices[i][1]] [0]); glVertex3fv(&vdata[tindices[i][2]] [0]);} glEnd(); Should be encapsulated in display list02/06/2003 15-462 Graphics I 24 Calculating the Normal VectorsCalculating the Normal Vectors Normalized cross product of any two sides GLfloat d1[3], d2[3], n[3];void icoNormVec (int i) { for (k = 0; k < 3; k++) {d1[k] = vdata[tindices[i][0]] [k] vdata[tindices[i][1]] [k];d2[k] = vdata[tindices[i][1]] [k] vdata[tindices[i][2]] [k]; }normCrossProd(d1, d2, n); glNormal3fv(n);}02/06/2003 15-462 Graphics I 25 The Normalized Cross ProductThe Normalized Cross Product Omitzero-checkforbrevityvoid normalize(float v[3]) {GLfloat d = sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]); v[0] /= d; v[1] /= d; v[2] /= d;}void normCrossProd(float u[3], float v[3], float out[3]) { out[0] = u[1]*v[2] u[2]*v[1];out[1] = u[2]*v[0] u[0]*v[2];out[2] = u[0]*v[1] u[1]*v[0];normalize(out); }02/06/2003 15-462 Graphics I 26 The IcosahedronThe Icosahedron Using simple lighting setup02/06/2003 15-462 Graphics I 27Sphere NormalsSphere Normals Setupinsteadtousenormalsofsphere UnitspherenormalisexactlyspherepointglBegin(GL_TRIANGLES); for (i = 0; i < 20; i++) {glNormal3fv(&vdata[tindices[i][0]][0]); glVertex3fv(&vdata[tindices[i][0]][0]); glNormal3fv(&vdata[tindices[i][1]][0]); glVertex3fv(&vdata[tindices[i][1]][0]); glNormal3fv(&vdata[tindices[i][2]][0]); glVertex3fv(&vdata[tindices[i][2]][0]);} glEnd();02/06/2003 15-462 Graphics I 28 Icosahedron with Sphere NormalsIcosahedron with Sphere Normals Interpolationvsflatshadingeffect02/06/2003 15-462 Graphics I 29 Recursive SubdivisionRecursive Subdivision Generalmethodforbuildingapproximations Researchtopic:constructagoodmesh Low curvature, fewer mesh points High curvature, more mesh points Stop subdivision based on resolution Some advanced data structures for animation Interaction with textures Here: simplest case Approximatespherebysubdividing icosahedron02/06/2003 15-462 Graphics I 30 Methods of SubdivisionMethods of Subdivision Bisecting angles Computing center Bisecting sides Here:bisectsidestoretainregularity02/06/2003 15-462 Graphics I 31Bisection of SidesBisection of Sides Drawifnofurthersubdivisionrequestedvoid subdivide(GLfloat v1[3], GLfloat v2[3], GLfloat v3[3], int depth){ GLfloat v12[3], v23[3], v31[3]; int i;if (depth == 0) { drawTriangle(v1, v2, v3); } for (i = 0; i < 3; i++) {v12[i] = (v1[i]+v2[i])/2.0; v23[i] = (v2[i]+v3[i])/2.0; v31[i] = (v3[i]+v1[i])/2.0;} …02/06/2003 15-462 Graphics I 32 Extrusion of MidpointsExtrusion of Midpoints Re-normalizemidpointstolieonunitspherevoid subdivide(GLfloat v1[3], GLfloat v2[3], GLfloat v3[3], int depth){ …normalize(v12);normalize(v23);normalize(v31);subdivide(v1, v12, v31, depth-1); subdivide(v2, v23, v12, depth-1); subdivide(v3, v31, v23, depth-1); subdivide(v12, v23, v31, depth-1);}02/06/2003 15-462 Graphics I 33 Start with IcosahedronStart with Icosahedron Insamplecode:controldepthwith+and-void display(void) { …for (i = 0; i < 20; i++) { subdivide(&vdata[tindices[i][0]][0],&vdata[tindices[i][1]][0], &vdata[tindices[i][2]][0], depth); }glFlush(); }02/06/200315-462 Graphics I 34One SubdivisionOne Subdivision 02/06/2003 15-462 Graphics I 35 Two SubdivisionsTwo Subdivisions Each time, multiply number of faces by 402/06/2003 15-462 Graphics I 36 Three SubdivisionsThree Subdivisions Reasonableapproximationtosphere02/06/2003 15-462 Graphics I 37 Example Lighting PropertiesExample Lighting PropertiesGLfloat light_ambient[]={0.2, 0.2, 0.2, 1.0}; GLfloat light_diffuse[]={1.0, 1.0, 1.0, 1.0}; GLfloat light_specular[]={0.0, 0.0, 0.0, 1.0};glLightfv(GL_LIGHT0, GL_AMBIENT, light_ambient); glLightfv(GL_LIGHT0, GL_DIFFUSE, light_diffuse); glLightfv(GL_LIGHT0, GL_SPECULAR, light_specular); 02/06/2003 15-462 Graphics I 38 Example Material PropertiesExample Material Properties GLfloat mat_specular[]={0.0, 0.0, 0.0, 1.0};GLfloat mat_diffuse[]={0.8, 0.6, 0.4, 1.0};GLfloat mat_ambient[]={0.8, 0.6, 0.4, 1.0};GLfloat mat_shininess={20.0};glMaterialfv(GL_FRONT, GL_SPECULAR, mat_specular); glMaterialfv(GL_FRONT, GL_AMBIENT, mat_ambient); glMaterialfv(GL_FRONT, GL_DIFFUSE, mat_diffuse); glMaterialf(GL_FRONT, GL_SHININESS, mat_shininess);glShadeModel(GL_SMOOTH); /*enable smooth shading */ glEnable(GL_LIGHTING); /* enable lighting */ glEnable(GL_LIGHT0); /* enable light 0 */02/06/2003 15-462 Graphics I 39 SummarySummary Polygonal Shading Light Sources in OpenGL MaterialPropertiesinOpenGL NormalVectorsinOpenGL Example: Approximating a Sphere02/06/2003 15-462 Graphics I 40 PreviewPreview Either Basic texture mapping Curves and surfaces02/06/2003 15-462 Graphics I 41