forum.alglib.net

I am not a mathematician but I would appeciate some assistance in how to model the following geometrical problem.

We have a rectangle with rounded corners that must fit within a circle (Not necessarily tangent edges of circle).

W Width of rectangle
H Height of rectangle
R Radius of rectangles corner
D Diameter of circle

Approximate domains:
W [10..100] Continuous or discrete range
H [10..100] Continuous or discrete range
R [1..100] Continuous or discrete range (Deliberately too large)
D [10,12,14,16,20,30] Discrete set

Constraints
C1 R < 0.5 W
C2 R < 0.5 H
(C3 (W-2R)^2 + (H-2R)^2 <= (D-2R)^2)

Replacing C3 by substitution with the following Constraints
C4 A=W-2R
C5 B=H-2R
C6 C=D-2R
C7 A^2 + B^2 <= C^2

We want to maximize/minimize each variable (typically W, H, R) for each diameter D

If we have understood it correctly, this is a QCLP - a linear objective function (single variable) with a mix of linear/quadratic equality/inequality constraints.

Note: This is just an example and we do know how to solve it manually of course - however we are trying to understand how such a model can be setup and solved in Alglib.