CS计算机代考程序代写 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 list
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Calculating the Normal Vectors
Calculating 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);
}
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The Normalized Cross Product
The Normalized Cross Product
• Omitzero-checkforbrevity
void 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); }
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The Icosahedron
The Icosahedron
• Using simple lighting setup
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Sphere Normals
Sphere Normals
• Setupinsteadtousenormalsofsphere
• Unitspherenormalisexactlyspherepoint
glBegin(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();
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Icosahedron with Sphere Normals
Icosahedron with Sphere Normals
• Interpolationvsflatshadingeffect
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Recursive Subdivision
Recursive 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 icosahedron
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Methods of Subdivision
Methods of Subdivision
• Bisecting angles • Computing center • Bisecting sides
• Here:bisectsidestoretainregularity
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Bisection of Sides
Bisection of Sides
• Drawifnofurthersubdivisionrequested
void 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;
} ...
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Extrusion of Midpoints
Extrusion of Midpoints
• Re-normalizemidpointstolieonunitsphere
void 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);
}
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Start with Icosahedron
Start 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(); }
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One Subdivision
One Subdivision
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Two Subdivisions
Two Subdivisions
• Each time, multiply number of faces by 4
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Three Subdivisions
Three Subdivisions
• Reasonableapproximationtosphere
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Example Lighting Properties
Example Lighting Properties
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[]={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);
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Example Material Properties
Example 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 */
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Summary
Summary
• Polygonal Shading
• Light Sources in OpenGL
• MaterialPropertiesinOpenGL
• NormalVectorsinOpenGL
• Example: Approximating a Sphere
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Preview
Preview
• Either
– Basic texture mapping – Curves and surfaces
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