CODEWITHSUNDEEP
javascriptmathtrigonometry
Jonathan Plackett
Jonathan Plackett

Reputation: 2426

Create a triangle around a point, perpendicular to a normal

I'd like get the points of a triangle around a point where the face would point in the direction of a specified normal. I'll be using THREE.js to add them to a BufferGeometry.

Very crude drawing:

Please forgive this very crude drawing

Here's the code I have so far:

//The XYZ location of a point:
var x = model.points[i*3];
var y = model.points[i*3+1];
var z = model.points[i*3+2];


//The normal vector direction:
var nx = model.normals[i*3];
var ny = model.normals[i*3+1];
var nz = model.normals[i*3+2];

How can I pick 3 more points around this point that are all perpendicular to the normal and the same distance from the point / each other?

THANKS!

Upvotes: 0

Views: 703

Answers (3)

junvar
junvar

Reputation: 11574

1) Take cross product of the normal with an arbitrary non-parallel vector. This will get you a vector perpendicular to the normal vector.

1.5) Normalize and scale the perpendicular vector to desired size. The length of this vector will be the distance from the triangle's centroid to each of its vertices.

2) Rotate the perpendicular vector by 2PI/3 and 4PI/3 around the normal vector.

3) Add the 3 vectors to the center point.

Upvotes: 1

Amr Berag
Amr Berag

Reputation: 1110

You need to find the plane parallel to the normal and containing the point (there is only one) and then pick any point in this plane with the specified distance and rotate it two times by 120 degree around the centeral point.

Upvotes: 0

Code-Apprentice
Code-Apprentice

Reputation: 83527

Note that there are infinitely many triangles that fit your criteria, even if we limit to only equilateral triangles. This is because there is an entire plane which is perpendicular to the given vector <nx, ny, nz> through the given point (x, y, z). Read here to see how to derive the equation for that plane. From there, you will need to pick a point on the plane. Then you can calculate the other two points by rotating around the given point at (x, y, z).

Upvotes: 0

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