Equation of a line that goes through A(−3,−7,−5)A(-3,-7,-5) and B(2,3,0)B(2,3,0) and find C(x,−1,z)C(x, -1, z) on the same line

Problem: Find the equation of a line that passes through A(−3,−7,−5) and B(2,3,0) and find C(x,−1,z) on the same line. I have completely forgotten how to solve this and I’ve been reading about how to solve this and it’s super confusing. How do I find the equation of this line? I’ve found the parametric, vector … Read more

Construct incenter of tetrahedron

How do I construct the incenter of a tetrahedron? Assuming that the tetrahedron in question is not regular/isoceles, of course. Answer The incenter is the intersection of the bisector planes of the dihedral angles formed by three tetrahedron faces which don’t have a common vertex. If $ABCD$ are your tetrahedron vertices, to obtain the bisector … Read more

3D Hilbert Curve Without Double-Length Edges?

Are there any 3D hilbert curves wherein there are no double-length edges? An example of a “double-length edge” would be the two sections outlined in red below: Answer In 3D, there are only three seven-segment polylines with vertices at the vertices of the unit cube and all segments axis-aligned, if we ignore their rotated and/or … Read more

Simplest way to determine if two 3D boxes intersect?

Given If given two sets of two points in 3D space (where they are defined to be the corners of the box): Box1: P1 = (961.46, 215.15, 1465.44) P2 = (970.02, 214.93, 1481.77) Translational Matrix for Box 1: Box2: P1 = (1093.52, -499.50, 896.11) P2 = (1093.12, -505.49, 878.68) Translational Matrix for Box 2: What … Read more

Plane through the intersection of two given planes.

If I have two planes r⋅ˆn1=p1r⋅ˆn2=p2 If they intersect somewhere then the intersection will form a line, if r′ is the position vector of a point on the intersection line then I have r′⋅ˆn1=p1r′⋅ˆn2=p2 If I combine these two equations I would get r′⋅(ˆn1+ˆn2)=p1+p2 This looks like a vector equation of a plane. But if … Read more

Find ellipse center from 3 points (in 3D) [closed]

Closed. This question does not meet Mathematics Stack Exchange guidelines. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for Mathematics Stack Exchange. Closed 8 months ago. Improve this question I have following problem: a camera detects 3 points with 3D coordinates, and I know all those … Read more

Volume of regular tetrahedron in a cube

Given a cube with side length $a$, a regular tetrahedron is constructed such that two vertices of the tetrahedron lie on the cube’s body diagonal and the other two vertices lie on the diagonal of one of the faces of the cube. Determine the volume of the tetrahedron. All I can do is to visualise … Read more

Is the value of π\pi in 2d the same in 3d? [closed]

Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for Mathematics Stack Exchange. Closed 8 years ago. Improve this question I am starting with my question with the note “Assume no math skills”. Given that, all down votes are welcomed. (At the … Read more