My implementation of the Dual-Contouring algorithm.
It samples the following implicit distance function:
rect_outer = Rectangle(0.0, 0.0, 0.5, 0.5)
rect_inner = Rectangle.from_corner(-0.5, -0.3, 0.3, 0.2)
c1 = Circle(-0.2, -0.2, 0.1)
c2 = Circle(0.2, 0.3*np.sin(np.deg2rad(theta*4)), 0.152)
sdf = Difference(rect_outer, rect_inner, c1, c2)
sdf = Rotate(sdf, theta)Starting with the samples, I construct the quadtree and calculate the vertices of the cells that contain the contour. To determine the vertex positions, I use a standard quadratic error function along with mass-points. Then, following the method from the original paper, I generate contour lines connecting these vertices. Once that's done, I balance the quadtree, ensuring neighboring cells have a depth difference of no more than 1. The meshing process happens in two steps: first, I mesh the cells without contour lines, and then handle the rest. After building the initial mesh, I apply Lloyd's relaxation to the vertices to enhance the overall mesh quality.