Grayscale to Red-Green-Blue (MATLAB Jet) color scale

Question

I was given a data set that is essentially an image, however each pixel in the image is represented as a value from -1 to 1 inclusive. I am writing an application that need

Answer 1

The other answers treat the interpolation as a piecewise linear function. This can be simplified by using a clamped triangular basis function for interpolation. We need a clamp function that maps its input to the closed unit interval:

And a basis function for interpolation:

Then the color becomes:

Plotting this from -1 to 1 gives:

Which is the same as provided in this answer. Using an efficient clamp implementation:

double clamp(double v)
{
  const double t = v < 0 ? 0 : v;
  return t > 1.0 ? 1.0 : t;
}

and ensuring your value t is in [-1, 1], then jet color is simply:

double red   = clamp(1.5 - std::abs(2.0 * t - 1.0));
double green = clamp(1.5 - std::abs(2.0 * t));
double blue  = clamp(1.5 - std::abs(2.0 * t + 1.0));

As shown in the above link on implementing clamp, the compiler may optimize out branches. The compiler may also use intrinsics to set the sign bit for std::abs eliminating another branch.

"Hot-to-Cold"

A similar treatment can be used for the "hot-to-cold" color mapping. In this case the basis and color functions are:

And the hot-to-cold plot for [-1, 1]:

OpenGL Shader Program

Eliminating explicit branches makes this approach efficient for implementing as an OpenGL shader program. GLSL provides built-in functions for both abs and clamp that operate on 3D vectors. Vectorizing the color calculation and preferring built-in functions over branching can provide significant performance gains. Below is an implementation in GLSL that returns the RGB jet color as a vec3. Note that the basis function was modified such that t must lie in [0,1] rather than the range used in the other examples.

vec3 jet(float t)
{
  return clamp(vec3(1.5) - abs(4.0 * vec3(t) + vec3(-3, -2, -1)), vec3(0), vec3(1));
}