2D usage is:

1. click on a face to specify the working plane. The face may be loose in the model, or may be nested in a group or component. This step is necessary because a triangle must lie in a plane, and the reference edge defined by the two click points below is not sufficient to define a unique plane. Once the plane is chosen, it will be remembered for solving additional triangles. It can be changed by shift-clicking on a new face.
2. click on the first end point of the reference side
3. type the length of the new side from that point then press return (enter)
4. click on the second end point of the reference side
5. type the length of the new side from the second point then press return (enter)

The extension will then draw two guide points, one at each of the possible solutions (or tell you if no solution is possible for the given data), and a guide line connecting the two points.

Repeat steps 2-5 (or shift-click at step 2 to define a new plane) to solve additional triangles.

3D usage is:

1. click the first vertex of a reference triangle
2. type the length from that point to the solution (radius of a sphere around that point) then press return (enter)
3. click the second vertex of the reference triangle
4. type the length from the second point to the solution then press return (enter)
5. click the third vertex of the reference triangle
6. type the length from the third vertex to the solution then press return (enter)

The extension will then draw two guide points, one at each of the two possible solutions (or tell you if no solution is possible for the given data), and a guide line connecting the two points

SB Trilateration

Trilateration involves finding triangles with three given side lengths. This is in contrast to triangulation, which uses the angles between the sides. Trilateration is appropriate for example when plotting surveys made with modern distance measuring equipment. It is also generally useful for finding precise intersections between circles or spheres.

This extension mathematically solves 2D and 3D trilateration problems in SketchUp without the need to draw circles or spheres in the model. The solutions use true circles and spheres, they are not affected by Sketchup's polygonal representations.

It adds a pair of guide points at the two possible solution vertices and a guide line connecting them to make them easier to find.

The 2D problem is: given a working plane, two reference points (implicitly the ends of a first reference side) and lengths for two additional sides, find the vertices of the two possible triangles using the edge between the points as one side and having the given lengths for the other two sides. There are two possible solutions because the triangle can be flipped around the reference edge.

2D usage is:

1. click on a face to specify the working plane. The face may be loose in the model, or may be nested in a group or component. This step is necessary because a triangle must lie in a plane, and the reference edge defined by the two click points below is not sufficient to define a unique plane. Once the plane is chosen, it will be remembered for solving additional triangles. It can be changed by shift-clicking on a new face.
2. click on the first end point of the reference side
3. type the length of the new side from that point then press return (enter)
4. click on the second end point of the reference side
5. type the length of the new side from the second point then press return (enter)

The extension will then draw two guide points, one at each of the possible solutions (or tell you if no solution is possible for the given data), and a guide line connecting the two points.

Repeat steps 2-5 (or shift-click at step 2 to define a new plane) to solve additional triangles.

The 3D problem is:

Given three reference points (implicitly, corners of a reference triangle) and a length measured from each of the three points, find the two points in space that are those distances from the points (the intersections of three spheres centered at the given points and having the given radii). There are two solutions because the answer can be mirrored around the plane of the reference triangle. The user must choose which one is the desired result.

Unlike the 2D case, the three points uniquely define a plane, so there is no need to separate select one.

3D usage is:

1. click the first vertex of a reference triangle
2. type the length from that point to the solution (radius of a sphere around that point) then press return (enter)
3. click the second vertex of the reference triangle
4. type the length from the second point to the solution then press return (enter)
5. click the third vertex of the reference triangle
6. type the length from the third vertex to the solution then press return (enter)

The extension will then draw two guide points, one at each of the two possible solutions (or tell you if no solution is possible for the given data), and a guide line connecting the two points

July 22, 2018: Version 1.0 initial release October 27, 2021: Minor update to cursors January 5, 2024: Version 1.1 fixed an issue with Ruby 3.2 as used since SketchUp 2024