Calculate point in 3d space, between two points at specific distance

Question

For a camera movement in three.js I need to calculate point C so to move the camera from point A to a certain distance dist to point B .

Answer 1

three.js has methods to do that very easily.

Assuming a , b , and c are instances of THREE.Vector3() ,

a.set( 2, 1, 4 );
b.set( 9, 4, 2 );

c.subVectors( a, b ).setLength( dist ).add( b );

three.js r.91

Answer 2

So you need to calculate the coordinates of point C , given that it lies on the line between B and A at the given distance from B ? This is pretty straightforward using the following steps:

• Calculate the vector from B to A (this will just be A - B ).
• Normalize that vector (make it's length 1).
• Multiply that by the distance you want.
• Add that vector to the point B .

So a short javascript example:

 const A = [2, 1, 4]; const B = [9, 4, 2]; const dist = 3; function addVectors(v1, v2) { return v1.map((x, i) => x + v2[i]); } function scalarMultiply(v, c) { return v.map(x => x*c); } function getLength(v) { return Math.hypot(...v); } const vecB2A = addVectors(A, scalarMultiply(B, -1)); // Step 1 const normB2A = scalarMultiply(vecB2A, 1/getLength(vecB2A)); // Step 2 const distB2A = scalarMultiply(normB2A, dist); // Step 3 const C = addVectors(B, distB2A); // Final step console.log(C); 

Answer 3

Point C is equal to point B minus 'dist' times a unit vector whose direction is AB. So it is quite easy:

vector v from A to B is equal (xB-xA, yB-yA, zB-zA) / distance(AB)

Then C = B - d*v where d is the distance from B you want C to be.