Back-Face Culling with Cross Products

Half Your Triangles Face Away

A closed 3D model has outward-facing front triangles and inward-facing back triangles. When the camera sits outside the mesh, back faces are never visible. They would be hidden by front faces and the z-buffer anyway.

Back-face culling skips rasterizing away-facing triangles. For closed opaque models, this eliminates roughly 50% of triangles before any per-pixel work begins. OpenGL, Vulkan, and Direct3D enable it by default.

The Cross Product Test

For triangle vertices A, B, C in counter-clockwise order (front-facing):

c
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For example, a triangle on the XY plane facing +Z with camera at (0,0,5) has N pointing toward the camera and survives. A triangle facing -Z gets culled because the normal points away. The dot product measures cosine of the angle between normal and view vector; negative means angle > 90 degrees.

CCW winding: convention for front faces in right-handed systems
Two-sided materials: disable culling or triangles vanish
Open surfaces: culling creates holes on single-sided geometry

For This Exercise

You will implement the culling test for a set of triangles and count survivors. This task requires computing face normals via cross product and comparing against the camera position. Wrong winding order when importing Blender or Maya meshes is one of the most common bugs in custom renderers.

Write a C program that implements back-face culling for a set of triangles.

Requirements:

Define a camera at position (0, 0, 5)
Define these triangles with CCW winding (front facing when looking down -z): T1: A=(0,0,0), B=(1,0,0), C=(0,1,0) — facing camera, should survive T2: A=(0,0,0), B=(0,1,0), C=(1,0,0) — CW winding, should be culled T3: A=(-2,0,-3), B=(-1,0,-3), C=(-2,1,-3) — behind camera plane, facing away T4: A=(2,0,1), B=(3,0,1), C=(2,1,1) — in front, facing camera
For each triangle:
- Compute edge vectors: e1 = B - A, e2 = C - A
- Compute normal: N = cross(e1, e2)
- Compute view vector: V = camera - A
- Compute dot product: N dot V
- Print the normal, dot product, and whether the triangle is culled or kept
Count and print the total number of triangles kept and culled
Explain why winding order matters for culling
Include a note about when culling should be disabled (transparency, two-sided materials)

Half Your Triangles Face Away

The Cross Product Test

For triangle vertices A, B, C in counter-clockwise order (front-facing):

c
Loading…

CCW winding: convention for front faces in right-handed systems
Two-sided materials: disable culling or triangles vanish
Open surfaces: culling creates holes on single-sided geometry

For This Exercise

Write a C program that implements back-face culling for a set of triangles.

Requirements:

Define a camera at position (0, 0, 5)
Define these triangles with CCW winding (front facing when looking down -z): T1: A=(0,0,0), B=(1,0,0), C=(0,1,0) — facing camera, should survive T2: A=(0,0,0), B=(0,1,0), C=(1,0,0) — CW winding, should be culled T3: A=(-2,0,-3), B=(-1,0,-3), C=(-2,1,-3) — behind camera plane, facing away T4: A=(2,0,1), B=(3,0,1), C=(2,1,1) — in front, facing camera
For each triangle:
- Compute edge vectors: e1 = B - A, e2 = C - A
- Compute normal: N = cross(e1, e2)
- Compute view vector: V = camera - A
- Compute dot product: N dot V
- Print the normal, dot product, and whether the triangle is culled or kept
Count and print the total number of triangles kept and culled
Explain why winding order matters for culling
Include a note about when culling should be disabled (transparency, two-sided materials)

Topic Overview

Half Your Triangles Face Away

The Cross Product Test

For This Exercise

Implementation Task

Progressive Hints

Resources

Open Source

Back-Face Culling with Cross Products

Topic Overview

Half Your Triangles Face Away

The Cross Product Test

For This Exercise

Implementation Task

Progressive Hints

Resources

Open Source