Formula for z axe in Inverse Kinematics JavaScript
For x axe: x + Math.cos(angle) * segment_length;
For y axe: y + Math.sin(angle) * segment_length;
For z axe: z + ???
Formula for z axe in Inverse Kinematics JavaScript
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If your angle is the angle between a line in the xy plane and the x axis in the xy plane (as it appears), then z is unchanged.
You may want spherical polar coordinates, which involves 2 angles, theta and phi. This wikipedia article explains all: Spherical Polar Coordinates.