TrueType fonts, created by Apple Computer and Adobe Systems, use quadratic Bzier curves, while PostScript fonts, created
Question:
TrueType® fonts, created by Apple Computer and Adobe Systems, use quadratic Bézier curves, while PostScript® fonts, created by Microsoft, use cubic Bézier curves. The cubic curves provide more flexibility for typeface design, but it is important to Microsoft that every typeface using quadratic curves can be transformed into one that uses cubic curves. Suppose that w(t) is a quadratic curve, with control points p0, p1, and p2.
a. Find control points r0, r1, r2, and r3 such that the cubic Bézier curve x(t) with these control points has the property that x(t) and w(t) have the same initial and terminal points and the same tangent vectors at t = 0 and t = 1. (See Exercise 20.)
b. Show that if x(t) is constructed as in part (a), then x(t) = w(t) for 0 ≤ t ≤ 1.
Data From Exercise 20
Explain why a cubic Bézier curve is completely determined by x(0), x'(0), x(1), and x'(1).
Step by Step Answer:
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald