Obtain the Cubic Bezier Curve equation for the control points P₀ = (0,0), P₁ = (2,5), P₂ = (5,1), P₃ = (7,3).
The cubic Bézier curve is defined by the formula: [ B(t) = (1-t)^3 P_0 + 3(1-t)^2 t P_1 + 3(1-t) t^2 P_2 + t^3 P_3, \quad 0 \le t \le 1 ] Given the control points: [ P_0 = (0,0), \quad P_1 = (2,5), \quad P_2 = (5,1), \quad P_3 = (7,3) ] The x-component of the curve, (x(t)), is: [ x(t) = (1-t)^3 \cdot 0 + 3(1-t)^2 t \cdot 2 + 3(1-t) t^2 \cdot 5 + t^3 \cdot 7 ] Expand each term step by step: 1. ((1-t)^3 \cdot 0 = 0) 2. (3(1-t)^2 t \cdot ________ _______ _________ ______ _____ ______ ___ _________ __________ __________.
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