# Tagged Questions

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### Mapping between two unknown 3D coordinate systems from common motion

Coordinate systems A and B are rigidly linked in an unknown way. The platform then moves and the motion vectors [RA|TA] and [RB|TB] are calculated in each coordinate system. They are parallel but not ...
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### Difference between Euclidean space and vector space?

I often hear them used interchangeably ... they are very complicated to make any use of. Wikipedia words: Euclidean space: One way to think of the Euclidean plane is as a set of points ...
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### is there a higher dimensional analogue of the first isogonic center?

I'm curious to know if, given four points $a, b, c, d$, you can always find a point $p$ such that last lines $pa, pb, pc, pd$ form equal angles pairwise. I'd also appreciate resources on 3d geometry ...
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### Partition of the 3d space with circles?

Does it exist a partition of the 3d space with circles of positive radium? I know the answer is no for a plane, but I can not transpose my demonstration to the space and I have no clue on how to do ...
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### 3D Game: Pitch Yaw Roll of a point

I have a flat elliptical plane and I'm trying to figure out how to represent it based on its direction. So I basically need to calculate its pitch, yaw, and roll. I have a camera at $C$, and a point ...
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### Why are the axis labelled as such in the 3d Cartesian coordinate system?

A long time ago I was taught that in 3d space, the x axis is the length/width or left/right space, the y axis is the height, and the z axis is the depth. When we draw things in 2d on a page, this ...
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### 3D Geometry Question

In $3$-dimensional Geometry, if angle made of line segment $OP$ with $X,Y,Z$-axis are in $1:2:3$, then what is the angle made by line segment with $Y$-axis? My Solution: Let $\alpha,\beta$ and ...
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### Finding intersection of 2 planes without cartesian equations?

The planes $\pi_1$ and $\pi_2$ have vector equations: $$\pi_1: r=\lambda_1(i+j-k)+\mu_1(2i-j+k)$$ $$\pi_2: r=\lambda_2(i+2j+k)+\mu_2(3i+j-k)$$ $i.$ The line $l$ passes through the point with ...
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### Why does aliasing cause loss of a degree of freedom in Euler angles?

I'm reading a book on 3D game math where the author points out that when using Euler angles the same orientation can be reached by doing two different operations; say rotating a cube 90 degrees around ...
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### calculate surface normal with random sampling of points

Given a surface in $R^3$ and a point P on the surface, I want to calculate the surface normal in this point, the vector that is perpendicular to the surface. However, I do not know the whole surface, ...
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### Euclidean Geometry a triangle problem

In the three dimensional figure below, is there a way to prove that $$\angle MNK = 90^ \circ$$ $\hspace{2.8in}$
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### Is there a formula for the solid angle at each vertex of tetrahedron?

A tetrahedron has four vertices as much as a triangle has three vertices. A tetrahedron therefore can have four solid angles as much as a triangle can have three angles. I am wondering: Is there a ...
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### How to calculate volume of 3d convex hull?

Convex hull is defined by a set of planes (point on plane, plane normal). I also know the plane intersections points which form polygons on each face. How to calculate volume of convex hull?
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### Projection of 5 skew lines

Given five skew lines, is it possible to find a point $P$ and a plane $\pi$ such that the projections of the five lines from $P$ onto $\pi$ intersect in the same point $Q$? [editet: rewritten clearly, ...
If I have three lines $a,$ $b$ and $c$ in the euclidean 3D space, which are pairwise non-coplanar, is there always a fourth line $x$, that intersects theses three lines?