I have a four-sided area defined by four arbitrary irregular edges (polylines) which I am trying to find a way for inverting an XY coordinate to a UV coordinate on. The space is mapped in a bilinear fashion, to where UV coordinates are mapped in an 'H' fashion, where the U coordinate is used to find a start/endpoint on both the top/bottom edges and then used to interpolate an intermediate curve between the left/right edges that the V coordinate can be used to find the final resulting XY coordinate. This forward computation from a UV coordinate to an XY coordinate is very straightforward, but computing the inverse: finding the original UV values for a given XY coordinate is anything but straightforward.
Basically, I'm looking for the inverse of this: https://upload.wikimedia.org/wikipedia/commons/3/3a/Bilinear_interpolation_curvilinear_coordinates.png
The closest thing I've found is this, for quadrilaterials: http://iquilezles.org/www/articles/ibilinear/ibilinear.htm
I can work with a solution that involves two linear edges if they're on opposite sides (i.e. only two opposing edges are arbitrary polylines/curves).
Any ideas? Thanks.
I love this coffee table. It has character in materials, its minimalist but quite functional. and its profile is curved, perfect to break up the angular, linear living room I have. However, I can't find it at taller than 11". Theres a 14" side table, but its much smaller in depth and length.
Anyone have a taller product? My searches are coming up dry!
The Pearson coefficient can be used to measure linear association. Is there any equivalent for non-linear (e.g., curvilinear) associations?
If so, how do I interpret it? Is it also on a -1 to 1 scale?