Finding a common interior point to two polygons
Suppose I have overlapping polygons. Neither is necessarily convex. What's an efficient algorithm to find a point interior to both of them and not on either's boundary?
Assuming that they overlap, and our polygons are defined by their sets of vertices in 3D.
Solution
A variant of the Vatti polygon clipping algorithm can be used. Vatti's algorithm is a scanline algorithm, which basically means scan over the vertices of both polygons, from (say) left to right, as well as over any intersections between their boundaries. Between the vertical lines passing through any consecutive two of these "events", you then examine the trapezoids/triangles created by the polygons. Once you find a trapezoid which is part of both, you can just output its centroid.
- Compute the area of intersection between a circle and a triangle?
- Behavioral difference between constructing a `Nef_polyhedron_3` directly from OFF file and constructing from a `Polyhedron_3` built from the same file
- Catmull-Rom interpolation on SVG Paths
- Intersection between AABB and a capsule (swept sphere)
- Compute minimum area convex k-gon in 2d
- Difference between algorithm solution and MATLAB CVX solution in Graphical LASSO?
- k-way triangle set intersection and triangulation
- How to find the intersection point of a 3D curve and a 3D surface?
- Extending a line segment to fit into a bounding box
- Find visibility polyhedron given a point inside it
- While finding count of points inside some shape using KD-Tree, do we need to check areas intersection, or just compare depth-appropriate properties?
- Check if a 3D point lies inside a 3D platonic solid?
- How to check a point is inside an ellipsoid with orientation?
- In solidworks, is there a way to get the direction cosines of a surface normal?
- How to find overlapping area of convex coplanar polygons in 3D?
- Compensate IMU pan/tilt
- derive (approximate) rotation transform matrix (numpy) on a unit sphere given a mapping of vectors (n=12)
- Find two furthest points in a point set in linear time (2-approximation algorithm)
- Difference between quadtree and kd-tree
- How do I compute, in O(n) time, a convex hull of a set of points which are sorted by x-coordinate?
- Check if a point projected on a line segment is not outside it
- Segment Intersection
- How to convert spherical geometry to ellipsoid geometry c++ vertex generation
- Closest edge to a rectangle in a plane of rectangles
- What is most efficient way to find the intersection of a line and a circle in python?
- Initializing Half-edge data structure from vertices
- How to draw a circle in GNU Octave
- Calculate the outline of an abstract shape with holes
- What is the algorithm for finding the center of a circle from three points?
- Fast footpoint computation over polygonal lines in MATLAB