15. Heatmap

The figure below is 100 pixels wide and 300 pixels tall. Each 100 pixel color segment is a color gradient.

For example, when y=150, the color produced is (make-color 0 175 0) because the color is supposed to be green when y is between 100 and 199.

1. Write a function heat-color: number(y) -> color that produces the correct color.

2. Write a function color-helper: number(x) number(y) -> color that just calls the heat-color function to get the correct color.

3. Use build-image to create the 100x300 rectangle pictured above.

4. Challenge. Modify your work on the graphing review so that the background is colored based on the distance a point (x,y) is from the graph of y=f(x).

   

Sketch of the challenge solution

1. The idea is to use the heat-color function that we wrote earlier.

    (define (color-outline-1 xc yc)
      (heat-color (- yc (f xc)))
   

   Unfortunately, xc is in computer coordinates, but f works only in people coordinates, so we need to add our conversion functions.

2. Change the use of f to the fc version that works in computer coordinates.

    (define (fc x)
      (yptyc (f (xctxp x))))))
   

3. Sometimes we get negative values and decimals, so add a fixer and use it in the color-outline function to fix the input to heat-color.

    (define (fixer v)
      (real->int (abs v)))
   

4. For more vivrant colors, multiply by two in the fixer (or modify the heat-color function).