# Questions tagged [3d]

For things related to 3 dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For non-planar geometry, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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### Jacobian of converting Euler angles to rotation vector or rotation matrix

please consider this paper: A Primer on the Differential Calculus of 3D Orientations - Bloesch 2016. Equations 27, 29 and 30, for example, give nice results about differentiating the rotation of a ...
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### Calculating the angle between 2 one-sided surfaces.

For a piece of software that I am writing, I need to determine the angle between two 3-dimensional one-sided surfaces that intersect at a line. The surfaces are defined as triangles with a normal ...
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### Show that $E,F,G,H,I$ lies on a sphere. [closed]

Let $ABCD$ a tetrahedron and $E,F,G,H,I,J$ on $AB,BC,CA,CD,DA,DB$ s.t. $AE\cdot EB=BF\cdot FC=CH\cdot HD=DI\cdot IA=AG\cdot GC=DJ\cdot JB$. Show that $E,F,G,H,I$ lies on a sphere. I know that is ...
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### Offset a point on a curve in 3D space

I have a curve AB in 3D space in which I know the start A(x,y,z) and end point B (x,y,z). Now, I have a point O (x,y,z) which should be moved along the curve for some distance (D). If it's a straight ...
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### The locus of a line in 3D passing intersecting two other lines

A line through any point on the curve $x^2-y^2=1 , z=0$ intersects two lines $y=x, z=1$ and $y=-x, z=-1$. Required is the locus of the line . Just to clarify(as I have seen people question), the above ...
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### Is there a better way to find the "outline" path for a set of points in $3D$ space?

I am trying to create a $3D$ model. In $3D$ model file formats, a face is defined by ordering the vertices of that face clockwise as viewed from the center of the object. I have a script that ...
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### Rotate a body to align z axis in a particular direction

I have the orientation of a body in world frame, $_wP_b$. Let us say, a bottle with the z axis representing the height, lying on its sides on the table. Now, I have a direction vector $\textbf{v}$, ...
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### In how many different ways can I draw them?

I have a cube and I draw a vertex, a middle of an edge and a diagonal of a face. In how many different ways can I draw them? Two cubes can look similar after a rotation. I don't know how to start.
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### Inverse of a roto-translation matrix in 3D space

I want to create two roto-translation matrices. The first transforms point $P$ into point $P'$ by performing a translation $T=(x_t, y_t, z_t)$ and two rotations (one around the $x$ axis of $\alpha$ ...
1 vote
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### In any 3d object, how do you calculate the rotation of that object so the visible part with most surface area is pointing to the camera/eye?

Example: Take a sphere and cut it in half. If you point the curved part of the half sphere to the camera its the visible part with most surface area
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### Possible to find rotation around x, y, z axes by knowing the polar angles $\phi, \theta$?

I'm working with a 3D cartesian system $\vec{e'_x},\vec{e'_y},\vec{e'_z}$ that moves around in a global coordinate system. I know the origo position and $\vec{e'_z}$ in global coordinates. There is no ...
1 vote
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### Equation of bisector between two straight lines given in symmetrical form [closed]

Please help in solving the attached question. I know in 2D, it is solved as $\dfrac{ax+by+c}{\sqrt{a^2+b^2}}=\pm \dfrac{px+qy+s}{\sqrt{p^2+q^2}}$ Not sure if we use the same formula for 3D? And if yes,...
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### How to get 3D coordinates (XYZ) of the sun given Azimuth and altitude/elevation?

I want to create an Augmented Reality(AR) application to show the sun's position where I need the 3D(XYZ) coordinates to plot in Augmented Reality(AR). Main question: I need to calculate the 3D ...
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### Rotating a vector to make it parallel to the z axis

I have to rotate the $P=(P_x,P_Y,P_z)$ point so that the $OP$ vector is parallel with respect to the $Z$ axis. To do this I perform 2 rotations, the first around the $Z$ axis and the second around the ...
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### Approximate 3D function that has certain points as peak

Given set of 3D points, how can I find a continuous function that has each point as the peak? You can imagine making a terrain editor that the inputs are 3D points and the output is a smooth mountain ...
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### Conditions on tetrahedron side lengths that guarantee existence of a sphere tangent to all its edges

I recently worked on the problem of finding a sphere tangent to the edges of an irregular tetrahedron. I found that if one of the triangular faces of the tetrahedron is an isosceles triangle, then it ...
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### Rotation of a frame reference with axis z lying on normal n

I am creating a rotation matrix capable of converting the reference system $A=(x_a, y_a, z_a)$ into a second reference system $B=(x_b, y_b, z_b)$ where the $x_b$ and $y_b$ axes lie in a plane with ...
1 vote
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### Rotate a Translation and a Quaternion around the z axis of an arbitrary pose by an angle theta

I need to implement a rotation in a program but it's 15 years I haven't used rigid body motion maths. I use poses that are described by a translation T and quaternion Q. Everything is expressed in the ...
Find the cosine of the angle between the planes $(A,B,C,D)$ and $(M,N,K)$ in the cube $ABCDA_1B_1C_1D_1$ where $M,N$ and $K$ are the midpoints of $BB_1,A_1B_1$ and $B_1C_1$, respectively. As we can ...