How deeply does Advanced Algorithms and Data Structures cover vector-to-vector product?

Develops the perpendicular-vector derivation and implementation of scaling factors, but does not extend beyond this planar intersection use.

Vector-to-vector product

As explained in 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.

A cross product helps determine whether two vectors are parallel. For two-dimensional segment vectors v = B − A and w = D − C, a nonzero result indicates that their supporting lines meet at one point; the intersection may still fall outside either segment. section 15.4.1

Use the vector operation to turn segment intersection into scalar checks:

Construct v from A to B and w from C to D. section 15.4.1

Testing two edges

The vectorScalingFactor method builds the segment vectors, forms a perpendicular vector, and returns a scalar factor. Calling it in both directions supplies h and g for edgesIntersection.

How Advanced Algorithms and Data Structures covers it

Cover of Advanced Algorithms and Data Structures

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Geometry for ProgrammersA vector product is an operation combining vectors, such as a dot product, cross product, or triple product, to produce a scalar or vector.

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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.

This explainer was generated by Manning's knowledge graph from the text of Advanced Algorithms and Data Structures. The section links point to the parts of the book it draws on.