Lines, Curves and Surfaces in 3D
Lines, Curves and Surfaces in 3D
Lines, Curves and Surfaces in 3D
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Angle Between a L<strong>in</strong>e <strong>and</strong> a Plane<br />
θ<br />
CM0268<br />
MATLAB<br />
DSP<br />
GRAPHICS<br />
524<br />
If the plane is <strong>in</strong> implicit form ax + by + cz + d = 0 <strong>and</strong> l<strong>in</strong>e is <strong>in</strong><br />
parametric form:<br />
x = x 0 + ft<br />
y = y 0 + gt<br />
z = z 0 + ht<br />
then the angle, γ between the l<strong>in</strong>e <strong>and</strong> the normal the plane (a, b, c)<br />
is:<br />
γ = cos −1 (af + bg + ch)<br />
The angle, θ, between the l<strong>in</strong>e <strong>and</strong> the plane is then:<br />
θ = π 2 − γ<br />
1<br />
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