Render Vector on GPU Supporting tagline
Reference
Basics
表示平面曲线的方程主要有
- 显函数方程：y=f(x)
- 隐函数方程(也叫一般方程)：F(x,y)=0
- 参数方程: x=x(t), y=y(t)
- 极坐标方程:
Parametric Curves
C(t) = t · C
The vector t contains power basis functions and C is the coefficient matrix that determines the shape of the curve. The rational curve C(t) has components [x(t) y(t) w(t)]. In the special case where w(t) = 1, we refer to C(t) as an integral curve. Commonly, the parameter t is restricted to the interval [0,1] and we think of C(t) as defining a curve segment.
Implicit Curves
TrueType curves are quadratic B-splines. Each spline is equivalent to a series of quadratic Bézier curves. And each of these is defined by 3 outline control points, rendered by a parametric, quadratic equation hard-coded into the rasterizer. If the 3 points of each Bézier curve are (Ax, Ay), (Bx, By) and (Cx, Cy), then
px = (1-t)2.Ax + 2t(1-t).Bx + t2.Cx
py = (1-t)2.Ay + 2t(1-t).By + t2.Cy
Varying the parameter t from 0 to 1 produces all the points p on the curve defined by A, B and C. #Quadratic Splines B-spline -> Bézier