Declaration

TRadialExGradientSampler = class(TCustomGradientLookUpTableSampler)

Description

TRadialExGradientSampler provides gradation of colors along a cylinder defined by two circles $(C_1,R_1)$ and $(C_2,R_2)$. Also knows as "two point conical gradient".

Clamp	Mirror	Repeat

Colors are mapped according to WrapMode.

Mathematics & Algorithm

Given focal center $C_1=(X_1,Y_1)$ and outer center $C_2=(X_2,Y_2)$, sampling parameter $t$ solves the quadratic intersection equation between the line segment from $C_1$ to $(X,Y)$ and the moving interpolated circle:

$$C(t)=C_1+t(C_2-C_1),R(t)=R_1+t(R_2-R_1)$$

Solving $\parallel (X,Y)-C(t){\parallel }^2=R(t{)}^2$ yields normalized gradient offset $u=t$.

References

• HTML Canvas Radial Gradients
• Microsoft Typography, COLR