How can I find a point placed between 2 points forming a segment using only the partial length of the segment?

Given 2 points A(x0,y0,z0) and C(x2,y2,z2) forming a segment of length "k", what is the equation to find a point C(x1,y1,z1) placed at "k-1" distance from A?

This is basic maths. If you already have classes handling vectors and points, you should be able to do something like this:

Vector direction = C - A;
direction.Normalize();
Point newpoint = A + (k-1) * direction;

You just need

• difference between points (gives a vector)

• scalar product of a float with a vector (gives a new vector)

• addition of a point and a vector (gives a new point)

Smells like homework, so, general idea, but no code:

Get the slope of AC for each coordinate set (x, y, and z). Then progress k-1 units from A at each of the calculated slope to get the coordinates of the new point.