David Luebke 04/21/23
CS 551 / 645: Introductory Computer Graphics
David Luebke
http://www.cs.virginia.edu/~cs551
David Luebke 04/21/23
Recap: OpenGL
OpenGL provides an interface and implementation for interactive rendering.
It has become a standard because:– A standard was badly needed– OpenGL is pretty good– SGI promoted it and Microsoft (sorta) bought in
OpenGl is particularly tuned to hardware-accelerated transformation, lighting, texturing, and Z-buffering
David Luebke 04/21/23
Recap: OpenGL Conventions
Functions in OpenGL start with gl (or glu) Function names indicate argument type/#
– E.g., glColor3f() vs glColor3fv() vs glColor4ub()
Geometry is specified as a list of vertices between glBegin() and glEnd() calls:
glBegin(GL_POLYGON);
glVertex3f(x1, y1, z1);
glVertex3f(x2, y2, z2);
glVertex3f(x3, y3, z3);
glEnd();
David Luebke 04/21/23
Recap: Miscellaneous OpenGL
The vertices of the front side of a polygon are ordered counterclockwise
You can draw multiple triangles between glBegin(GL_TRIANGLES) and glEnd()
The GL_TRIANGLE_STRIP primitive reduces redundancy by sharing vertices:
v0v2
v1v3
v4
v5
David Luebke 04/21/23
Miscellaneous OpenGL
The GL_TRIANGLE_FAN primitive is another way to reduce vertex redundancy:
v0
v1
v2
v3v4
v5
v6
David Luebke 04/21/23
Recap: OpenGL Lighting
OpenGL binds our Phong lighting coefficients (ka, kd, ks, nshiny) into materials
Calling glMaterialfv() sets a single attribute of the current material
Example: float green[] = {0, 1, 0, 1};
float white[] = {1, 1, 1, 1};
glMaterialfv(GL_FRONT, GL_DIFFUSE, green);
glMaterialfv(GL_FRONT, GL_SPECULAR, white);
David Luebke 04/21/23
Recap: OpenGL Lighting
OpenGL supports at least 8 lights, with parameters set by the glLight() call:
float l_amb [] = {.1, .1, .1, 1.0};
float l_diff[] = {1, 0, 0, 1};
float l_spec[] = {1, 1, 1, 1};
float l_pos[] = {10, 100, 30, 0};
glLightfv(GL_LIGHT0, GL_AMBIENT, l_amb);
glLightfv(GL_LIGHT0, GL_DIFFUSE, l_diff);
glLightfv(GL_LIGHT0, GL_SPECULAR, l_spec);
glLightfv(GL_LIGHT0, GL_POSITION, l_pos);
(the 4th coordinate in l_pos is 0.0 for a directional light, 1.0 for a point light)
lights
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Errata: OpenGL Lighting
Recall the Phong lighting model:
OpenGL modifies this slightly:
– Each light contributes separately to ambient term
– Lights have a separate intensity for specular reflection
(Why might this be useful?)
lights
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sdi
ambientatotal
shiny
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David Luebke 04/21/23
OpenGL: Lighting
Don’t forget to enable lighting and each light:glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0); Can set the lighting model too:
– Intensity of the ambient light source– Whether to treat eye point as infinitely far away– Whether to perform lighting calculations for both
sides of polygons– All these things have reasonable default values– man glLightModel for details
David Luebke 04/21/23
OpenGL: Display Lists
OpenGL can “compile” a series of rendering commands into a display list...
glNewList(1, GL_COMPILE);
glBegin(GL_TRIANGLES);
glVertex3fv(v0);
/* draw lots of triangles… */
glVertex3fv(v2);
glEnd();
glEndList();
…which can be rendered with a single call:glCallList(1);
David Luebke 04/21/23
OpenGL: Display Lists
Display lists can contain:– Geometry– Color, material, and texture specifications– Matrix transforms (up shortly)– Other display lists!
Display lists are not only handy, they usually increase performance– Why might OpenGL be able to render a series of
commands faster if they have been compiled into a display list?
David Luebke 04/21/23
OpenGL: Matrix Manipulation
OpenGL keeps two matrices that vertices are multiplied by upon calling glVertex()– The modelview matrix combines all modeling
transforms and the viewing transform– The projection matrix performs the projection (usually a
perspective projection)– Various commands affect the current matrix– You need to specify which matrix is current:
E.g., glMatrixMode(GL_MODELVIEW) or glMatrixMode(GL_PROJECTION)
– glLoadIdentity() replaces the contents of the current matrix with the identity matrix
David Luebke 04/21/23
OpenGL: Modeling Transforms
Some OpenGL commands generate transformation matrices:
glTranslatef(Tx, Ty, Tz);
glRotatef(angleDegrees, Ax, Ay, Az);
glScalef(Sx, Sy, Sz);
The resulting matrix concatenates to the right of the current matrix
David Luebke 04/21/23
OpenGL: Modeling Transforms
Example:glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glTranslatef(…);
glRotatef(…); Result: the modelview matrix is set to:
I • T • R == T • R
which then multiplies all following vertices– Thus transformations appearing last in the program
have the first effect on the geometry
David Luebke 04/21/23
OpenGL: Viewing Transforms
Viewing transforms are treated the same way Ex: gluLookAt() computes a lookat matrix
and concatenates it with the current matrix: gluLookAt(eyeX, eyeY, eyeZ,
centerX, centerY, centerZ,
upX, upY, upZ);– Again, this matrix postmultiplies the current matrix– Should gluLookAt() be called first or last?
David Luebke 04/21/23
OpenGL: Projection Transforms
The projection matrix is generally used for the perspective projection matrix– Why do you suppose OpenGL separates the
modelview and projection matrices?
gluPerspective() creates a projection matrix similarly to the call in assignment 6
gluPerspective(double FOVy, double aspect,
double near, double far);
– FOVy: field of view (°) in the y vertical (y) direction aspect: viewport width (y) divided by height (x)
David Luebke 04/21/23
The Scene Graph
Recall the concept of instancing, or using the same geometry for multiple objects– Example: 4 wheels on car– How might we use display lists for instancing?
Compile geometry (say a car tire, centered about the origin) into a display list
Set up matrices: viewing transform + modeling transform(s) to put origin at front left corner of car
Call display list for tire Set up matrices, this time putting origin at front right of car Call display list for tire [Etc…]
– Why is this inefficient?
David Luebke 04/21/23
The Scene Graph
Answer: because many objects in a scene typically share multiple transformations
The scene graph captures transformations and object-object relationships in a DAG:
Robot
BodyHead
ArmTrunkLegEyeMouth
Objects
Instancing(i.e, a matrix)
Legend
World
David Luebke 04/21/23
The Scene Graph
Traverse the scene graph in depth-first order, concatenating and undoing transforms:– For example, to render the robot:
Apply robot head matrix Apply head mouth matrix
– Render mouth Un-apply head mouth matrix Apply head left eye matrix
– Render eye Un-apply head left eye matrix Apply head right eye matrix
– Render eye Un-apply head right eye matrix
Un-apply robot head matrix Apply robot body matrix
How should we implement this
“un-apply” business?
David Luebke 04/21/23
The Scene Graph in OpenGL
OpenGL maintains a matrix stack of modeling and viewing transformations:
ArmTrunkLegEyeMouth
Head Body
Robot
Foot
MatrixMatrixStackStack
VisitedVisited
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ActiveActive
David Luebke 04/21/23
OpenGL: The Matrix Stack
The user can save the current transformation matrix by pushing it onto the stack with glPushMatrix()
The user can later restore the most recently pushed matrix with glPopMatrix()
These commands really only make sense when in GL_MODELVIEW matrix mode
David Luebke 04/21/23
OpenGL: Matrix Stack Example
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glTranslatef(…);
// save translation matrix:
glPushMatrix();
glRotatef(…);
// render something translated & rotated:
glCallList(foo);
// restore pushed matrix, undoing rotation:
glPopMatrix();
// render something else, no rotation:
glCallList(bar);
David Luebke 04/21/23
Coming Up:
Animation: smooth (flicker-free) motion using double buffering
More OpenGL tricks– Backface culling– Gouraud shading– Computing vertex normals
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