Simplicial Interpolation
This software lets you specify a correspondence between points in two Euclidean spaces ℝd and ℝe, to then smoothly interpolate between them. For instance, this lets a mouse (d = 2) or a gamepad's pair of joysticks (d = 4) manipulate dozens or hundreds of parameters.
It implements simplicial interpolation, as described in
Interpolated Mappings for Musical Instruments,
published in Organised Sound 7(2):85‒96, © Cambridge U. Press.
This software is licensed under the MIT License, © 2022 Camille Goudeseune,
except for code from Ken Clarkson's hull.shar, which is © 1995 AT&T
and whose license is similar to the MIT License.
How to build and self-test
On Windows 10 or 11, install Windows Subsystem for Linux, using the Ubuntu 20 or Ubuntu 22 distro.
On Linux, Windows, or macOS 10.3+ (2003+), make test
How to run the demo
On Linux or Windows, sudo apt install freeglut3-dev g++ libgl-dev libgl1-mesa-dev make
.
On Mac, brew install freeglut
.
- On Windows, install an X server such as VcXsrv.
make demo
, or, to specify the high dimension e (say, 20) and the number of points (say, 100),./glut 20 100
- Move the mouse around over the window. If you like, zoom with the scroll wheel.
- To exit, hit q or the escape key.
The mouse pointer q
("query") is interpreted as a weighted sum
of the corners of its surrounding triangle.
The size of each point's gray disc shows its weight.
The special center point C
is used for an unbounded simplex
(a triangle with one edge at infinity),
when q
lies outside the points' convex hull.
History
This was published in 2002 at http://zx81.isl.uiuc.edu/interpolation/ (defunct), revised slightly in 2009, and moved to GitHub in 2018.