Find the intersection of a line with a plane: Difference between revisions
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⍝ The intersection I belongs to a line defined by point D and vector V, means that t exists, so that I = D + tV |
⍝ The intersection I belongs to a line defined by point D and vector V, means that t exists, so that I = D + tV |
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⍝ I belongs to the plan defined by point P and normal vector N. This means that the IP vector is normal to vector N |
⍝ I belongs to the plan defined by point P and normal vector N. This means that the IP vector is normal to vector N |
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⍝ This translates to their scalar product |
⍝ This translates to their scalar product being zero. |
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⍝ (P - I).N = 0 <=> (P - D - tV).N = 0 |
⍝ (P - I).N = 0 <=> (P - D - tV).N = 0 |
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⍝ Using distributivity, then associativity, the following equations are established: |
⍝ Using distributivity, then associativity, the following equations are established: |
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