Algorithm (Workflow)

This function, PLcirclearc, calculates two circle arcs between two points on a circle, following the right-hand rule. It is part of the SolidGeometry library.

Input Parameters

• cp: Center point of the circle or radius (R) with a sign indicating direction.
• A: Point A on the circle or angle w1.
• B: Point B on the circle or angle w2.

Output Results

• PLR: Right-hand arc starting at A (red).
• PLL: Left-hand arc starting at B (green).

Algorithm Steps

1. If cp is a scalar, it is treated as the radius (R). The midpoint m between A and B is calculated, and the vector eab from A to B is determined.
2. The unit vector e1 is derived from eab, and o1 is the perpendicular vector to e1.
3. The angle w is calculated as half the angle subtended by A and B at the circle's center, and d is the distance from m to the center point cp.
4. The center point cp is recalculated using m, d, and o1.
5. Vectors e1 and e2 are calculated from cp to A and B, respectively.
6. The radius R is determined from the norm of e1.
7. An error is raised if A and B are not equidistant from cp.
8. Angles w1 and w2 are calculated using atan2 for vectors e1 and e2.
9. Adjust w1 and w2 to ensure they are positive and w2 is greater than w1.
10. Calculate the right-hand arc PLR using the function PLcircle with parameters R, w2-w1, and w1, then add cp.
11. Calculate the left-hand arc PLL by flipping the result of PLcircle with parameters R, w1-w2+2*pi, and w2, then add cp.
12. If no output is specified, plot the points and arcs using SGfigure and PLplot, with annotations for PLR and PLL.