A large particle with radius r hits the plane with perpendicular 'n' and passing through ,q'. I need to check whether it hits the plane or not. In order to do that I need to find the point of contact. My question is: we should shorten the 'p' by r to get the point of contact?
particle with radius 'r' hits the plane. what is the point of contact?
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vector-spaces
3d
1 Answers
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If you represent the particle position by the position of the center of the particle, you can move the plane by one radius along the normal. The particle contacting the plane is the same as the center being in the new plane.
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0Without moving the plane how can I find the contact? Can I add the radius r to center of particle p? – 2012-09-17
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0@BadSniper: yes, you can add a length $r$ vector to the point $p$, oriented along the normal to the plane. The result is the same. – 2012-09-17
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0How do I add r? Its a scalar. P is a point. – 2012-09-17
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0@BadSniper: that's why I said a length $r$ vector along the normal to the plane. If $\vec n$ is a unit normal to the plane, you have $p+r\vec n$ – 2012-09-17
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0we have to normalize the orthogonal n and multiply it with r? – 2012-09-17
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0@BadSniper: yes. What you are trying to find is when $p$ is exactly $r$ away from the plane in the perpendicular direction. – 2012-09-17