Explanation Explanation Given : T u × T v = 〈 1 , 2 , 2 〉 at a sample point in the rectangle. Size of rectangle is 0.01 × 0.02 Formula Used: ∬ S d S = ∬ D ‖ T u × T v ‖ d A Calculations: T u × T v = 〈 1 , 2 , 2 〉 ‖ T u × T v ‖ = 1 2 + 2 2 + 2 2 ‖ T u × T v ‖ = 1 + 4 + 4 ‖ T u × T v ‖ = 9 ‖ T u × T v ‖ = 3 Given that Size of rectangle is 0.01 × 0.02 . Hence Total Area A = 0.01 × 0.02 = 0...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.4, Problem 3PQ

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A parameterization maps a rectangle of size $0.01 \times 0.02$ in the uv-plane onto a small patch S of a surface. Estimate Area(S) if $T_{u} \times T_{v} = 〈 1, 2, 2 〉$ at a sample point in the rectangle.

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Chapter 17.4, Problem 2PQ

Chapter 17.4, Problem 4PQ

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Chapter 17 Solutions

CALCULUS (CLOTH)

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A parameterization maps a rectangle of size 0.01 × 0.02 in the uv- plane onto a small patch S of a surface. Estimate Area( S ) if T u × T v = 〈 1 , 2 , 2 〉 at a sample point in the rectangle.

Solution Summary: The author explains how the parameterization maps a rectangle of size 0.01 0.02 in the uv- plane onto the small patch S of the surface.

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To determine:

A parameterization maps a rectangle of size $0.01 \times 0.02$ in the uv-plane onto a small patch S of a surface. Estimate Area(S) if $T_{u} \times T_{v} = 〈 1, 2, 2 〉$ at a sample point in the rectangle.

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Chapter 17 Solutions

A parameterization maps a rectangle of size 0.01 × 0.02 in the uv- plane onto a small patch S of a surface. Estimate Area( S ) if T u × T v = 〈 1 , 2 , 2 〉 at a sample point in the rectangle.

Solution Summary: The author explains how the parameterization maps a rectangle of size 0.01 0.02 in the uv- plane onto the small patch S of the surface.

Concept explainers

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To determine: A parameterization maps a rectangle of size 0.01×0.02 in the uv-plane onto a small patch S of a surface. Estimate Area(S) if Tu×Tv=〈1,2,2〉 at a sample point in the rectangle.

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Chapter 17 Solutions

To determine:

A parameterization maps a rectangle of size $0.01 \times 0.02$ in the uv-plane onto a small patch S of a surface. Estimate Area(S) if $T_{u} \times T_{v} = 〈 1, 2, 2 〉$ at a sample point in the rectangle.