Find a transformation from u,v space to x,y,z space that takes the triangle U = [(0,0),(1,0),(0,1)] to the triangle T=[(1,0),-2),(-1,2,0),(1,1,2)]

aortiH

aortiH

Answered question

2021-01-02

Find a transformation from u,v space to x,y,z space that takes the triangle U=[001001] to the triangle
T=[(1,0),2),(1,2,0),(1,1,2)]

Answer & Explanation

averes8

averes8

Skilled2021-01-03Added 92 answers

Step 1
The triangle U=[001001] and the triangle
T=[102120112]
Step 2
Consider T(u,v)=(a1u+b1v+c1,a2u+b2v+c2,a3u+b3v=c3) .Obtain the transformation from u, v to x, y, z as
T(0,0)=(a1(0)+b1(0)+c1,a2(0)+b2(0)+c2,a3(0)+b3(0)+c3)
T(0,0)=(c1,c2,c3)
T(0,0)=(1,0,2)
c1=1,c2=0,c3=2
Step 3
Further evaluate as,
T(1,0)=(a1(1))+b1(0)+c1,a2(1)+b2(0)+c2,a3(1)+b2(0)+c3)
T(0,0)=(a1+c1,a2+c2,a3+c3)
T(0,0)=(1,2,0)
a1=c1=1,a2+c2=2,a3+c3=0
a1=2,a2=2,a3=2
Step 4
Also evaluate,

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