1. School of Computer Science
Computer Graphics
(fall,2010)
School of Computer Science
University of Seoul
Minho Kim

2. Chapter 3 Additional Drawing Tools

3. What to Learn Orthographic projection Viewport
Homogeneous coordinate systems
Matrix stack
(Clipping)
Representations of curves

4. sample03.c
To change the (orthographic 2D) camera setting dynamically – translation & zooming
How can we rotate the camera?
What types of cameras are supported?
What is the default camera setting?
What does the projection matrix do?
How can we make the image flipped vertically/horizontally?
How can we achieve the same effect using glMultMatrix?

5. Matrix Stacks The top element denotes current matrix state
Four stacks: modelview, projection, texture, and color
Different (minimum) stack depth for each
Stored in column-major format
Operations
glLoadIdentity, glLoadMatrix, glPushMatrix, glPopMatrix, glMultMatrix, etc.
Can handle hierarchical transformation (modelview) – How?

6. Homogeneous Coordinate System
Represents a 3D vectors/points as a 4-tuple: (x,y,z,w)
Corresponds to the vectors/points in the Cartesian coordinate system as (x,y,z,w)=(x/w,y/w,z/w)
w=0 for vectors and w≠0 for points
Can represent a translation as a matrix.
Can represent a perspective projection.
More in Chapter 4

7. Clipping
How to (efficiently) clip a line segment against an axis-aligned rectangle? → “Cohen-Sutherland clipper”

8. Representations of Curves
Implicit form
“Set of points (x,y) satisfying the equation f(x,y)=0”
Ex) x2+y2-r2=0
Parametric form
“Trace of points (x(t),y(t)) as t changes”
Ex) x(t)=r cos(t), y(t)=r sin(t)
Pros and cons?
How can we convert one to another?
How can we plot them?
More in Chapter 4