pack-priv Class PaintHelper

We use the plane equation to automatically map the ImagePattern image to the geometry being rendered. The shader uses two separate plane equations that take the (x,y) location (in device space) of the fragment being rendered to calculate (u,v) texture coordinates for that fragment: u = Ax + By + Cz + Dw v = Ex + Fy + Gz + Hw For the 3D case we calculate a perspective vector by projecting rays at various points, can finding the deltas. So we need to calculate appropriate values for the plane equation constants (A,B,D) and (E,F,H) such that {u,v}=0 for the top-left of the ImagePattern's anchor rectangle and {u,v}=1 for the bottom-right of the anchor rectangle. We can easily make the texture image repeat for {u,v} values outside the range [0,1] by using the fract() instruction within the shader. Calculating the plane equation constants is surprisingly simple. We can think of it as an inverse matrix operation that takes device space coordinates and transforms them into user space coordinates that correspond to a location relative to the anchor rectangle. First, we translate and scale the current user space transform by applying the anchor rectangle bounds. We then take the inverse of this affine transform. The rows of the resulting inverse matrix correlate nicely to the plane equation constants we were seeking.

This method uses techniques that are nearly identical to those employed in setGradientPaint() above. The primary difference is that at the native level we use a fragment shader to manually apply the plane equation constants to the current fragment position to calculate the gradient position in the range [0,1] (the native code for GradientPaint does the same, except that it uses OpenGL's automatic texture coordinate generation facilities). We Also, project in the 3D case to create a perspective vector which is used in the fragment shader. One other minor difference worth mentioning is that setGradientPaint() calculates the plane equation constants such that the gradient end points are positioned at 0.25 and 0.75 (for reasons discussed in the comments for that method). In contrast, for LinearGradientPaint we setup the equation constants such that the gradient end points fall at 0.0 and 1.0. The reason for this difference is that in the fragment shader we have more control over how the gradient values are interpreted (depending on the paint's CycleMethod).

This method calculates six m** values and a focus adjustment value that are used by the native fragment shader. (See LinearGradient Comment for the 3D case.) These techniques are based on a whitepaper by Daniel Rice on radial gradient performance (attached to the bug report for 6521533). One can refer to that document for the complete set of formulas and calculations, but the basic goal is to compose a transform that will convert an (x,y) position in device space into a "u" value that represents the relative distance to the gradient focus point. The resulting value can be used to look up the appropriate color by linearly interpolating between the two nearest colors in the gradient.