trace_ray: Compute the intersection points of a ray and a set of...

In cornelmpop/Lithics3D: A toolbox for 3D analysis of archaeological lithics

Compute the intersection points of a ray and a set of triangles

Description

Computes the intersection point(s) of a ray and an arbitrarily large set of triangles using the algorithm of Moller and Trumbore (1997).

Usage

trace_ray(o, d, v0, v1, v2, epsilon)

Arguments

o	A non-empty matrix (N x 3) with the coordinate of the ray origin repeated so that the number of rows (N) matches the number of triangles.
d	A non-empty matrix (N x 3) object with the direction of the ray (i.e. the difference between an arbitrary point along the line and the x, y, and z coordinate of the ray's origin) repeated so that the number of rows (N) matches the number of triangles.
v0	A non-empty matrix (N x 3) object with the (x,y,z) coordinates of the first vertex for each of the N triangles.
v1	A non-empty matrix (N x 3) object with the (x,y,z) coordinates of the second vertex for each of the N triangles.
v2	A non-empty matrix (N x 3) object with the (x,y,z) coordinates of the third vertex for each of the N triangles.
epsilon	The floating point precision used to check whether the angle formed by the ray and the plane of the triangles is +/- zero (i.e. whether the ray is parallel).

Value

a (N x 3) matrix containing the coordinates of the intersection points. If no intersections are found the output matrix will have zero rows.

Note

This function was inspired by the Matlab toolbox developed by Jaroslaw Tuszynski (2011-2014). In theory this function can be used as-is to test the intersection of multiple rays/multiple triangles, but in practice doing so requires much more memory (nr. triangles * nr. rays) and offers very marginal improvements in execution speed.

Examples

ray <- data.frame(x1=c(1.8), y1=c(4), z1=c(2),
                  x2=c(1.8), y2=c(4), z2=c(4.5))
triangles <- data.frame(x1=c(2,2), y1=c(3,3), z1=c(0,2),
                       x2=c(1,1), y2=c(5,5), z2=c(0,2),
                       x3=c(2,2), y3=c(4,4), z3=c(0,2))
o <- as.numeric(ray[1,1:3])
d <- as.numeric(ray[1,4:6]) - o
# Replicate ray to match the number of triangles:
o <- rbind(o, o)
d <- rbind(d, d)
# Prepare triangle data:
v0 <- as.matrix(triangles[,1:3])
v1 <- as.matrix(triangles[,4:6])
v2 <- as.matrix(triangles[,7:9])
# Set epsilon value:
epsilon <- .Machine$double.eps
trace_ray(o, d, v0, v1, v2, epsilon)

cornelmpop/Lithics3D documentation built on Feb. 10, 2024, 11:54 p.m.