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

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” http://www.vis.uni-stuttgart.de/ger/research/pub/pub2003/eg2003-diepstraten.pdf

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

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

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: http://worldofescher.com Klein bottle: http://alem3d.obidos.org/i/kbottle/kbc1.jpg * also called orientable manifold

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

Culling of Solids cos(theta) = n . e_3

Culling for non-closed surfaces no culling culling used inappropriately

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