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?
02/06/2003 15-462 Graphics I 2
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]
02/06/2003 15-462 Graphics I 18
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
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