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Examples of geometry calculations for computer graphics.

Vectors

• Normalize / unit vector
• Dot product as projection
• 2D cross product
• Angle between two vectors
• Rotate a point around a pivot

Lines & points

• Distance between two points
• Line midpoint
• Point along a line (lerp)
• Closest point on a line segment
• Perpendicular distance from a point to a line
• Line-segment intersection
• Reflect a point across a line
• Reflect a line off another line

Circles

• Circumference point
• Circles collision distance
• Point-in-circle (hit test)
• Circle ↔ circle intersection
• Circle ↔ line intersection
• Tangent lines from an external point
• Circumcircle of three points
• Reflect a line off a circle
• Triangle incircle
• Incircle & circumcircle together
• Apollonius problem (3-circle tangent)

Triangles

• Point-in-triangle (barycentric)
• Triangle signed area & winding

Polygons

• Point-in-polygon (ray casting)
• Polygon area & centroid (shoelace)
• Axis-aligned bounding box
• Convex hull (gift wrap)
• Polygon collision (SAT)

Random sampling

• Uniform random point in a circle
• Uniform random point in an annulus
• Uniform random point in a triangle

Distance fields

• SDF of a circle
• SDF of a box
• SDF smooth min (blob union)