The (3d) tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For geometry that is not on a plane, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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1answer
298 views

Identifying 3D shape from matrices analytically

I have a set of matrices (a 3D matrix, that represents a quantized body), for instance: (the size 5x5 here is just an example, the real size is a lot higher) $ M_1 = \left[ {\begin{array}{cc} 0 ...
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1answer
52 views

Linear transformations and primitive search in 3D

This question is about differentiation in $\mathbb{R}^3$. Let $V : \mathbb{R}^3 \to \mathbb{R}$ be a smooth enough function, $f:\mathbb{R}^3\to\mathbb{R}^3$ its gradient, and $M$ a $3\times 3$ real ...
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1answer
192 views

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, ...
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2answers
2k views

How do I map a 3D triangle into 2D?

The problem I'm having is mapping a 3D triangle into 2 dimensions. I have three points in x,y,z form, and want to map them onto the plane described by the normal of the triangle, such that I end up ...
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1answer
735 views

Find out the border of a planar figure for given a set of points – 2D case

Original post is edited after getting some suggestions; I am looking for a fast algorithm which is able to detect outer most boundary of a plane for given set of points. Suppose, I have 3D point ...
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1answer
150 views

Reconstructing a ring from a stack of 2D images (radially aligned)

I have a stack of images (about 180 of them) and there are 2 black dots on every single image. Hence, the position(x,y) of the two stars are provided initially. The dimensions of all these images are ...
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1answer
65 views

Find the form of $f(x,y)$ knowing the form of contour lines in the $XZ$ and $YZ$ planes

I am trying to find the form of $z=f(x,y)$. I know that: Contour lines in the $XZ$ plane are of the form: $$z=A*ln(x)+B$$ (the $A$ and $B$ parameters vary with $y$) Contour lines in the $YZ$ plane ...
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1answer
666 views

Plane intersecting line segment

I have a plane which is represented as a 3d point $\vec{p}$ with a normal $\hat{n}$. I also have a line segment specified by two points $\vec{v_1},\vec{v_2}$ . I want to get the intersection point (if ...
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1answer
140 views

Creating random triangles with points on the radius of a sphere and passing through center

I'm trying to create a pointy "ball" in 3d space using triangles. I want each triangle to pass through a sphere's center, with each point lying on the surface. I can easily make points on the ...
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3answers
612 views

Formula for gallons in a trough

I have a trough which is a circular container. How do I determine how many gallons of water it takes to fill up the trough? I was thinking that we measure the height and the width but I think it's a ...
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4answers
322 views

Term for Tetrahedron with Three Right Angles at a Point

Is there a name for the tetrahedron/pyramid (four vertices, four triangular faces, six edges) where three edges meet orthogonally at a point? Three of the faces are right triangles. Another ...
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1answer
370 views

Finding the radius of the largest sphere possible between a corner and another sphere

In a 3 dimensional Cartesian plane there is a sphere A that is in the first octant and is tangent to all coordinate planes. Now, imagine we want to find the another sphere B also tangent to all ...
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1answer
555 views

Coordinates of point on a line defined by two other points with a known distance from one of them

I have two points in 3D space; let's call them $A=(a_x, a_y, a_z)$ and $B=(b_x, b_y, b_z).$ Now, I need to place a third point, let's call it $C=(c_x, c_y, c_z)$, which lies on the line between $A$ ...
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1answer
260 views

Projecting a 3D vector to a screen, with the size $X\times Y$?

I am currently programming something, and I'm stuck on how to take a 3D vector, then project it on a screen. Say $X_s$ = the screen width and $Y_s$ = the screen height, Pa = pitch and $Y_a$ = yaw, ...
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1answer
486 views

quaternion representation of the rotation of a sphere into plane displacement

I do have a sphere of known radius which does have a coordinate frame rigidly attached to it. Let's call the coordinate frame attached to the sphere XYZs. The sphere can be rotated and displaced ...
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1answer
224 views

Keeping camera and focal point relative after translation

I'm creating a program that has a 3D view. The 3D world uses three vectors (X,Y,Z). Now, the way the camera works is by having two points, the focal point and the camera. The camera is set to look ...
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3answers
832 views

Largest Triangle with Vertices in the Unit Cube

How would one find a triangle, with vertices in or on the unit cube, such that the length of the smallest side is maximized? And what is that length? A lower bound for the length is $\sqrt{2}$, by ...
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4answers
7k views

Calculate distance in 3D space

Imagine I want to determine the distance between points 0,0,0 and 1,2,3. How is this calculated?
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1answer
1k views

Subtract gravity from 3D object in different orientations

I'm currently working on a project that involves calculating a sensor module's distance and orientation. The problem I'm running into is the fact that once the sensor is, for example, rotated around ...
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8answers
31k views

Recommended (free) software to plot points in 3d

I am looking for (preferably free) software to: 1) plot 3d points read from a file. A scatter plot would be fine. 2) Optionally color the points by a property - also read from the file It would be ...
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1answer
413 views

Torus: Circle cut

Given a Torus $T$ with major and minor radius $R$ and $r$, respectively, I can obtain a circle lying in $T$ by cutting $T$ with a bi-tangential plane. Now I don't want circles, but Tori with major ...
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1answer
511 views

Automation of 3D Paper Modeling

I recently saw this creative paper contraption online this prior weekend and wanted to see if I could automate the process of creating all ~35 layers of an equation. Essentially what I would want the ...
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1answer
732 views

Determining which side of a 3D cube is facing the viewer

Me and a friend are trying to render a rotating cube on a 2D plane(the screen) using java. Here's the problem The cube has 6 sides, each with a specific normal vector of the form (0,0,1), (0,-1,0) ...
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1answer
2k views

Distance from a point to circle's closest point

So let's assume I have a point $P$ in $3d$ space $(x_0, y_0, z_0)$. And I have a circle $C$ that is centered at $(x_1, y_1, z_1)$ with a radius $r$. I need to find the distance from $P$ to the nearest ...
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1answer
533 views

how to perform a rotation around a point which itself is rotating?

I'm working on rotating human limbs in a 3d game. I use Linear Algebra matrix rotations and translations to achieve moving the human and limbs. I currently can rotate around a pivot point by first ...
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0answers
207 views

Gauss interpolation in 3D and friends

I was looking for approaches on how to adequately interpolate the values for a continuous 3D function for which I have the exact values in a 3D grid of equidistant points. I found that linear ...
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2answers
227 views

How to calculate the rotation of an object wrt container, which itself is rotated wrt universe, so that the object has nil rotation wrt universe?

Long subject, so I am hoping that explains what I am asking, but still let me elaborate with an example. Let us assume we have an object as part of a container. Now the container is rotated by ...
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1answer
526 views

Find minimum in a constrained three-variable equation

After my last question I have worked through the math quite a bit and now I'm stuck again. This time my question is less wordy. I have two equations for $t$, one with respect to each $a_{x}$ and ...
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2answers
1k views

calculating perpendicular and angular distance between line segments in 3d

I originally posted this over at stackoverflow and they suggested asking it over here. link to original: ...
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2answers
1k views

Combining Two 3D Rotations

Every rotation in 3D space can be defined by a rotation axis and an angle. Now let's say we have two rotations R1(axis1, angle1), R2(axis2, angle2). I remember that Rotation operator is closed under ...
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3answers
569 views

Three non-coplanar lines in the 3D-space always have a fourth one that intersect them all?

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?
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0answers
56 views

Scale-agnostic, differentiable, co-planarity measure

I am looking for an (almost everywhere) differentiable function $f(p_1,p_2,p_3,p_4)$ that given four points will give me a scale-agnostic measure for co-planarity. It is zero if the four points lie on ...
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1answer
989 views

calculating coordinates from a flattened 3D array when you know the size, index and ordering

If I have a grid that I know is RxCxD in size, and I have number that corresponds to an element in that grid, and the grid is mapped in Row major format, how can I find out the ordered triplet that ...
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1answer
163 views

Differentiable orthogonal 3D vector

Does anybody know a simple and differentiable function that converts a 3D vector u = (x, y, z) to another vector that is orthogonal to ...
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1answer
950 views

Help with matrix mathematica

Hi I am wondering how best to explain this, I am working with WebGL (effectively OpenGL) and I have the ray cast from clicking in 3d space. I have the far and near values of the ray cast, the camera ...
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1answer
587 views

Intersection of spherical caps

Short version: if two spherical caps of the same sphere intersect, how can I determined the coordinates of the two "singular points" of this intersection Long version: On a unit sphere, centered at ...
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2answers
8k views

How to find shortest distance between two skew lines in 3D?

If given 2 lines $\alpha$ and $\beta$, that are created by 2 points: A and B 2 plane intersection I want to find shortest distance between them. $$\left\{\begin{array}{c} P_1=x_1X+y_1Y+z_1Z+C=0 ...
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1answer
612 views

Hyperbolic geometry. 3 dimensions. What is not well understood?

According to Mathworld, hyperbolic geometry is well understood in 2 dimensions but not in 3 dimensions. http://mathworld.wolfram.com/HyperbolicGeometry.html What isn't well understood about ...