This package provides features for geometric calculation. Before reading the code in geometry package, please understand these words.

Cartesian Coordinate System

Generally, it is also called a rectangular coordinate system or orthogonal coordinate system. In geometry package, we treat 3-dimension cartesian coordinate system with x,y,z axis.

Frenet Coordinate System

The frenet coordinate system is a coordinate system that is defined along a curve. In the geometry package, a curve consisted of 3 3rd order polynomials about each x,y, and z axis in a cartesian coordinate system. We define the shape of the curve by changing s value of the 3rd order polynomials as^3+bs^2+cs+d in range s = [0,1]. In this coordinate system, s value is normalized in range s = [0,1], s value does not consider the length when the curve is stretched.

If the coefficient a,b = 0, the shape of the curve is a line segment. In this case, the position of the s = 0 is the start point, and the position of the s = 1 is the end position.

If the coefficient a,b,c = 0, the shape of the curve is a point. In this case, only s = 0 case is valid, all of the other cases are invalid. If you find a case that the shape is a point but s is not equal to 0, please notify to developers.

Some of functions in the geometry package have denormalize_s argument with bool type. If the denormalize_s = false, the return value s of the function is normalized and in range s = [0,1]. If the denormalize_s = true, the return value s is denormalized and it returns the value s times the length of the curve.

Warning

A catmull-rom spline curve consists of multiple hermite curves. Each hermite curve has a different length. So, the catmull-rom spline curve can not normalize its length and frenet coordinate of catmull-rom spline curve is always denormalized.