Is Your Point Inside a Non-Regular Tetrahedron?

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To determine if a point lies inside a non-regular tetrahedron, one effective method is to calculate the volumes of sub-tetrahedra formed with the point and the tetrahedron's vertices. If the sum of these sub-tetrahedral volumes equals the volume of the original tetrahedron, the point is inside. This approach is analogous to checking point inclusion in a triangle by comparing areas. Additional resources and formulas for volume calculations can be found online. This method provides a reliable solution for the problem presented.
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Hello ,
does anybody knows how can I check if a point is inside a tetrahedral. The tetrahedral isn't regular.

Thanks!
 
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I don't know if this is a good way to solve it. But if in a triangle, the easiest way to check if a point is inside is to check the sum of the area. i.e. for ABC, there is a point P, if P is inside ABC, then, area(ABP)+area(ACP)+area(BCP) = area(ABC).

You can check the volume in the tetrahedral case.
 
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