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Math Calculus CALCULUS (CLOTH)

a)The Bezier curve defined by x ( t ) = a 0 ( 1 − t ) 3 + 3 a 1 t ( 1 − t ) 2 + 3 a 2 t 2 ( 1 − t ) + a 3 t 3 And y ( t ) = b 0 ( 1 − t ) 3 + 3 b 1 t ( 1 − t ) 2 + 3 b 2 t 2 ( 1 − t ) + b 3 t 3 with control points p 0 = ( 1 , 4 ) , p 1 = ( 3 , 12 ) , p 2 = ( 6 , 15 ) and p 3 = ( 7 , 4 ) has parametrization c ( t ) = ( 1 + 6 t + 3 t 2 − 3 t 3 , 4 + 24 t − 15 t 2 − 9 t 3 ) with its control points parametrization . b) the slope at t=0 is equal to the slope of segment p 0 p 1 ¯

a)The Bezier curve defined by x ( t ) = a 0 ( 1 − t ) 3 + 3 a 1 t ( 1 − t ) 2 + 3 a 2 t 2 ( 1 − t ) + a 3 t 3 And y ( t ) = b 0 ( 1 − t ) 3 + 3 b 1 t ( 1 − t ) 2 + 3 b 2 t 2 ( 1 − t ) + b 3 t 3 with control points p 0 = ( 1 , 4 ) , p 1 = ( 3 , 12 ) , p 2 = ( 6 , 15 ) and p 3 = ( 7 , 4 ) has parametrization c ( t ) = ( 1 + 6 t + 3 t 2 − 3 t 3 , 4 + 24 t − 15 t 2 − 9 t 3 ) with its control points parametrization . b) the slope at t=0 is equal to the slope of segment p 0 p 1 ¯

Solution Summary: The author explains that the Bezier curve defined by x ( t ) = a 0 ( 1

CALCULUS (CLOTH)

CALCULUS (CLOTH)

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 12.1, Problem 73E

To determine

To show:a)The Bezier curve defined by $x (t) = a_{0} {(1 - t)}^{3} + 3 a_{1} t {(1 - t)}^{2} + 3 a_{2} t^{2} (1 - t) + a_{3} t^{3}$

And $y (t) = b_{0} {(1 - t)}^{3} + 3 b_{1} t {(1 - t)}^{2} + 3 b_{2} t^{2} (1 - t) + b_{3} t^{3}$ with control points $p_{0} = (1, 4)$ , $p_{1} = (3, 12)$ , $p_{2} = (6, 15)$ and $p_{3} = (7, 4)$ has parametrization $c (t) = (1 + 6 t + 3 t^{2} - 3 t^{3}, 4 + 24 t - 15 t^{^{2}} - 9 t^{3})$

with its control points parametrization .

b) the slope at t=0 is equal to the slope of segment $\bar{p_{0} p_{1}}$

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Chapter 12.1, Problem 72E

Chapter 12.1, Problem 74E

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Chapter 12 Solutions

CALCULUS (CLOTH)

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E Ch. 12.1 - Prob. 11E Ch. 12.1 - Prob. 12E Ch. 12.1 - Prob. 13E Ch. 12.1 - Prob. 14E Ch. 12.1 - Prob. 15E Ch. 12.1 - Prob. 16E Ch. 12.1 - Prob. 17E Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Prob. 20E Ch. 12.1 - Prob. 21E Ch. 12.1 - Prob. 22E Ch. 12.1 - Prob. 23E Ch. 12.1 - Prob. 24E Ch. 12.1 - Prob. 25E Ch. 12.1 - Prob. 26E Ch. 12.1 - Prob. 27E Ch. 12.1 - Prob. 28E Ch. 12.1 - Prob. 29E Ch. 12.1 - Prob. 30E Ch. 12.1 - Prob. 31E Ch. 12.1 - Prob. 32E Ch. 12.1 - Prob. 33E Ch. 12.1 - Prob. 34E Ch. 12.1 - Prob. 35E Ch. 12.1 - Prob. 36E Ch. 12.1 - Prob. 37E Ch. 12.1 - Prob. 38E Ch. 12.1 - Prob. 39E Ch. 12.1 - Prob. 40E Ch. 12.1 - Prob. 41E Ch. 12.1 - Prob. 42E Ch. 12.1 - Prob. 43E Ch. 12.1 - Prob. 44E Ch. 12.1 - Prob. 45E Ch. 12.1 - Prob. 46E Ch. 12.1 - Prob. 47E Ch. 12.1 - Prob. 48E Ch. 12.1 - Prob. 49E Ch. 12.1 - Prob. 50E Ch. 12.1 - Prob. 51E Ch. 12.1 - 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