There are two main approaches. If you have a set of polygonal shapes, it is possible to create a BSP tree for each shape, then the BSP trees can be merged. From Wikipedia, 1990 Naylor, Amanatides, and Thibault provide an algorithm for merging two bsp trees to form a new bsp tree from the two … Read more
Here is a go at the implementation of your algorithm. I tweaked it quite a bit, but I think it does basically the same thing. Bounding circles I used a trick to make the computation more regular. Instead of segments defining the bounding box, I used circles with “infinite” radii, that can be considered a … Read more
I’d replace the bottomBoundary etc. with a decomposed transformation matrix (rotation, scale, translation) and use multitouch in the UI. When sliding a single finger over the image, you can update the translation component of the matrix, and with 2 fingers transform it so that the image appears to stick to the fingers. If you want … Read more
I didn’t know this trick before, but I think I understand it. The bottom border isn’t square, it’s beveled on the sides. A left border would be beveled on the top and bottom. This is so borders of different colors meet cleanly. Because the arrow element has 0 height and width, the border segment is … Read more
If you can, do the picking on the CPU by calculating a ray from the eye through the mouse pointer and intersect it with your models. If this isn’t an option I would go with some type of ID rendering. Assign each object you want to pick a unique color, render the objects with these … Read more
Convert the path to a polygon of arbitrary precision, and then calculate the area of the polygon. Interactive Demo: Area of Path via Subdivision (broken) At its core the above demo uses functions for adaptively subdividing path into a polygon and computing the area … Read more
Based on the last approach on this page, you can simply generate a vector consisting of independent samples from three standard normal distributions, then normalize the vector such that its magnitude is 1: import numpy as np def sample_spherical(npoints, ndim=3): vec = np.random.randn(ndim, npoints) vec /= np.linalg.norm(vec, axis=0) return vec For example: from matplotlib import … Read more
It’s possible to check if a point is inside a sector with only integer arithmetic and the basic operations of addition, subtraction and multiplication. For a point to be inside a circular sector, it has to meet the following tests: It has to be positioned counter-clockwise from the start “arm” of the sector. It has … Read more
I think it’s easiest to think of your problem as an intersection problem: what is the parameter location (s,t) where the point p intersects the arbitrary 2D bilinear surface defined by p0, p1, p2 and p3. The approach I’ll take to solving this problem is similar to tspauld’s suggestion. Start with two equations in terms … Read more