Question

Find the geometric coefficients of a cubic Hermite curve satisfying P0(1,1), P1(5,1), Pᵤ(0.5) = (93.5,0), and Pᵤu(0.5) = (0, -10).

A) (a, b, c, d)
B) (c, d, a, b)
C) (b, a, d, c)
D) (d, c, b, a)

Answer 1

A cubic Hermite curve can be represented by an equation. By substituting the given points into the equation and solving for t, we can find the geometric coefficients of the curve.

Step-by-step explanation:

A cubic Hermite curve can be represented by the equation:

P(t) = (1-3t^2+2t^3)P0 + (3t^2-2t^3)P1 + t(1-2t+t^2)Pᵤ + t^2(3t-2t^2)Pᵤu

Given the points P0(1,1), P1(5,1), Pᵤ(0.5) = (93.5,0), and Pᵤu(0.5) = (0, -10), we can substitute these values into the equation:

93.5 = (1-3t^2+2t^3) + 93.5t + 0t^2 - 10t^2

Simplifying the equation and solving for t, we can find the geometric coefficients of the cubic Hermite curve.