21 lines
1.0 KiB
Markdown
21 lines
1.0 KiB
Markdown
#rs/notes #rs/class/math163
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- 3D lines
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- can be described as parametric
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- symmetric equation of 3D line $$ \frac{x-x_{0}}{a} = \frac{y-y_{0}}{b} = \frac{z-z_{0}}{c}$$
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- In this case, the direction vector is $<a, b, c>$
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- Distance between a point and a line
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- Is the shortest distance between the two
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- This is the segment perpendicular to the line
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- In 2D, you have to take random point on the line
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- then project vector from this point to point not on the line onto the line to find where the closest point on the line is
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- ![[Pasted image 20251014183240.png]]
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- In this parallelogram, we know the area is equal to either $v \times PM$ or the base * the height (the height is the distance beween M and the line
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- This gives the formula $$d=\frac{||PM \times v ||}{||v||}$$ For the distance between point M and the line
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- Lines in 3D
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- Can either be parallel, intersection, the same line or skew
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- skew is when they don't intersect but aren't parallel either
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- Planes in 3D
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- defined by the normal vector of the plane
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