Introduction to Gradients

The Functions

At the top of the function area are 5 radio controls that let you select with which color channel you are working.
The RGB button (or YUV if you are performing calculations in that colorspace) operates on the 3 color channels locked together. If anything disagrees for either the x or y axis the function will be displayed as dashes, as it is in this screenshot for the y axis.
The A button selects the Alpha channel, which controls the opacity of the gradient and can be operated on in the same manner as the colors.

The next row of controls set parameters for the coordinate system. In the Cartesian coordinate system only the first parameter, rotation, has any effect. The value is specified in hundreds of degrees, ie 4500 represents 45 degrees.
The next two rows select the mathematical function to be applied in the x and y axis respectively. To the left are examples of each function and its effect on the gradient.
The first parameter is the multiplier, it controls how many times the function repeats over the width or height of the gradient. A value of 1 causes a single transition from (in the case of the x coordinate) the left colors to the right colors. A value of 2 causes the function to first go from the left colors to the right colors, and then back to the left colors. To the top right are examples of 3 multipliers.
The next two parameters control the left and right (or top and bottom) shelving. Increasing either value causes the respective edge of the transition to move inward. The sum of these two values cannot exceed 255, if it does both are ignored. The bottom right shows the effect of 4 sets of values.

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