algorithm - Efficient method for parameterizing distances between points in a 2D -


we have been developing small simple "cad" solution allow parameterize width , length of specific, simple shapes.

for instance consider following set of vertices forming triangle. 2 points form line. changing distances between point changing width of line.

triangle

we have discussing rigorously how approach problem.

things have discussed are:

  1. maintain list of equations of relationship between vertices. have point a, b, c. let w user-defined parameter. constraint equation shape bebx = ax + w, by = ay, , cx = bx , on.

the complexity enormous works.

  1. maybe model each vertex node in graph...?

what proper approached used in field?

i think trying implement simplified geometric constraint solver. basically, points location determined solving set of nonlinear equation (i.e., constraints) boundary conditions (i.e., points location known). if case, not easy when geometries involved 2d points , constraints involved distances between points. anyway, in field, implementing numeric solver via minimization typical approach. more general solution involve mix of numeric solver , algebraic solver.

here link contains lot of information constraint solver, including geometric constraint solver. hopefully, can find useful here.


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