使用距原点的距离作为第三个参数，确定由两个 3D 点定义的线上任意点的 x、y、z 坐标？

Question

If we have two points in 3D space, does C# have any high-level libraries that would return the x,y,z coordinates of a point that is a specified distance along the line defined by the two points, using one of the points as origin?

     extrapolatedPoint = FindPoint( origin3dPoint, second3dPoint, distanceFromOrigin)

PS The line defined by the points isn't a line-segment with the two points as endpoints, but a line that passes through the points.

Answer 1

Calculate unit direction vector (perhaps there are ready-to-use functions in C# math library - I see Vector.Normalize if it's suitable)

dx = P2.x - P1.x
dy = P2.y - P1.y
dz = P2.z - P1.z
Len = sqrt(dx*dx+dy*dy+dz*dz)
dx /= Len 
dy /= Len 
dz /= Len 

Now you can define point at line with distance D from the first point (in direction of P2 !) as

x  = P1.x + D * dx
y  = P1.y + D * dy
z  = P1.z + D * dz

Note that there are two points with distance D from the origin on the line, so I emphasized direction.