1. Inside-Outside & Culling
Introduction to Computer Graphics
CSE 470/598 Arizona State University
Dianne Hansford

2. Rendering Polygons A polygon has two sides
front & back
front is outward normal side
Can render front & back differently
Great for cutaways
Figure from Diepstraten et. al. “Interactive Cutaway Illustrations”

3. Polygons: Front & Back
Convention: front facing polygon vertices appear counterclockwise (ccw) on the screen 3
back facing 3 2 1
front facing 1 2
outward facing normals

4. Front Facing Polygon Eye coordinates v2 n v1 e3 Eye at origin
Looking at geometry down –z axis 3 v2
e3 ¢ n >= 0
 outward facing n v1 1 2 e3

5. Solids Closed geometry called a solid
Reasonable solids* can be constructed from polygons of consistent orientation
sphere, torus, ...
Opaque closed surface: no back facing polygons visible
Moebius strip/Klein bottle – not orientable
Escher’s Moebius strip:
Klein bottle:
* also called orientable manifold

6. Culling Culling is another form of clipping
removing polygons from the pipeline
speed up rendering
Culling removes back facing polygons
makes sense for solids
example: back facing polygons of a sphere
Happens in NDC coordinates

7. Culling of Solids
cos(theta) = n . e_3

8. Culling for non-closed surfaces
no culling
culling
used inappropriately

9. OpenGL & Culling glEnable(GL_CULL_FACE) glDisable(GL_CULL_FACE)
glCullFace(GL_BACK)
Also: GL_FRONT, GL_FRONT_AND_BACK
glFrontFace(GL_CCW) (default)
Also: GL_CW