This is a simple demonstration tool for use in a classroom while teaching lessons on parametric equations, linear interpolations (LERPs) and splines.  More functionality and educational content including mathematical basis for LERPs and splines and the ability to combine multiple cubic splines will be added in the future.  The tool will be complete and ready for use for the Fall 2020 semester.

A LERP and Spline Primer

Linear Interpolations

LERP is a shortening of the phrase linear interpolation, a mathematical method for finding a value that lies somewhere in between to other values.  One can think of a LERP as a weighted average with a parameter, t, representing the balance of the weighting of the two end-point values.  Consider two values A and B. These two values can be scalar values such as health points, engine rpms, or mass; they could be vector values such as force, velocity, or position ; or they could be any other quantifiable value such as an RGBA color.  The parameter , t, represents the balance of how much A versus how much B we mix to produce our interpolated value, Q.  When t is zero, we want Q to be all A with no amount of B.  Likewise, when t is one, we want Q to be all B with no amount of A.  Mathematically, we can represent this by the following equation

Q = (1-t)*A + t*B.

Smoothly increasing the parameter t from zero to one will smoothly transition Q from A to B.  This structure will be the basis of the splines we will construct next.

Quadratic Splines

...coming soon.

Cubic Splines

...coming soon.

Development log

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