Vector-to-vector product
A vector-to-vector product is an operation combining two vectors according to a defined rule to produce a scalar or another vector.
Geometry for Programmers
A vector product is an operation combining vectors, such as a dot product, cross product, or triple product, to produce a scalar or vector.
- How it is used
- Supports applied-geometry algorithms by converting vectors into scalars or vectors for angles, projections, areas, and volumes.
- How deep it goes
- Defines three products, explains their geometric roles, and applies them to plane, triangle, and segment distance calculations.
- Examples
- Uses translated and scaled point-vector models, parallelepiped heights, triangle planes, and point-to-segment distance calculations.
- What you can do after
- Build geometric algorithms for plane, triangle, and segment distances, including signed distance calculations.
Read how Geometry for Programmers explains vector-to-vector product →
Advanced Algorithms and Data Structures
The cross product is a vector operation in three-dimensional space whose result is perpendicular to its two operand vectors and whose magnitude depends on their sine-separated area.
- How it is used
- Checks whether two straight-line segments intersect by testing vector parallelism and solving their intersection parameters.
- How deep it goes
- Develops the perpendicular-vector derivation and implementation of scaling factors, but does not extend beyond this planar intersection use.
- Examples
- Uses segment endpoints A, B, C, and D, the equation B + h·v = D + g·w, and vectorScalingFactor and edgesIntersection.
- What you can do after
- Apply the operation to implement planar segment-intersection checks using perpendicular vectors and bounded scaling factors.
Read how Advanced Algorithms and Data Structures explains vector-to-vector product →
Related concepts
- vectorkind of · A vector is an ordered collection of components representing an element of a vector space.
- triple productused by · The triple product is the scalar obtained by taking the dot product of one vector with the cross product of two other vectors, equal to the signed volume of their parallelepiped.
- determinantuses · A determinant is a scalar computed from a square matrix that characterizes properties such as invertibility and signed volume scaling.
- point-in-triangle predicateused by · A point-in-triangle predicate determines whether a point lies inside, on the boundary of, or outside a specified triangle.
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