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Questions tagged [3d]

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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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I have one triangle in $3D$ space that I am tracking in a simulation. Between time steps I have the previous normal of the triangle and the current normal of the triangle along with both the current ...
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The volume of a cone with height $h$ and radius $r$ is $\frac{1}{3} \pi r^2 h$, which is exactly one third the volume of the smallest cylinder that it fits inside. This can be proved easily by ...
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Just like we have the equation $y=mx+b$ for $\mathbb{R}^{2}$, what would be a equation for $\mathbb{R}^{3}$? Thanks.
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I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. ...
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As the title says, i want to project 3D points with known (x, y, z) coordinates into a 2D plane with (x', y') coordinates, knowing that the x and y axes are respectively identical to the x' and y' ...
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Is there any pathological shape that has a finite surface area but an infinite volume, sort of like the opposite of a Gabriel's horn?
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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. $$\left\{\begin{array}{c} P_1=x_1X+y_1Y+z_1Z+C=0 \\ ...
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Suppose you have an arbitrary triangle with vertices $A$, $B$, and $C$. This paper (section 4.2) says that you can generate a random point, $P$, uniformly from within triangle $ABC$ by the following ...
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I am having a hard time figuring out if a 3D point lies in a cuboid (like the one in the picture below). I found a lot of examples to check if a point lies inside a rectangle in a 2D space for example ...
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It should be simple, but I'm having trouble. The three points are $$A(1,-2,1)\qquad B(4,-2,-2)\qquad C(4,1,4)$$ The plane I get is $$x+2y+z+6=0$$ but it obviously does not pass through the three ...
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I'm trying to model a smooth path between several control points in three dimensions, the problem is that there doesn't appear to be an explanation on how to use splines to achieve this. Are splines a ...
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The shape can be constructed by taking a cylinder with its height equal to its diameter and cutting a triangle out of it when viewing it from the side with the base of the triangle matching one end of ...
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What is the matrix expression of the rotation matrix in 3D which turns a vector $\vec{a}$ into a vector $\vec{b}$, with both vectors given by their coordinates? ($\vec{a} = (a_x, a_y, a_z)$ and $\vec{...
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Find an equation of a plane that passes through $p(1,5,1)$ and is perpendicular to planes $2x+y-2z = 2$ and $x+3z=4$. I basically need the 2 other points to make the vector and perform the cross ...
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I have 3 points in space A, B, and C all with (x,y,z) coordinates, therefore I know the distances between all these points. I wish to find point D(x,y,z) and I know the distances BD and CD, I do NOT ...
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Given two vectors in $\mathbb{R}^n$, $v_0$ and $v_1$, which define a plane including the origin a rotation along that plane can be defined from $v_0$ to $v_1$. I know the formula for rotation within ...
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I googled around a bit, but usually I found overly-technical explanations, or other, more specific Stackoverflow questions on how 3D computer graphics work. I'm sure I can find enough resources for ...
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I have an ellipsoid centered at the origin. Assume $a,b,c$ are expressed in millimeters. Say I want to cover it with a uniform coat/layer that is $d$ millimeters thick (uniformly). I just realized ...
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In 3D, given three points $P_1$, $P_2$, and $P_3$ spanning a non-degenerate triangle $T$. How to determine if the projection of a point $P$ onto the plane of $T$ lies within $T$?
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I don't really know what to search up to answer my question. I tried such things as "ellipse matching" and "3d circle orientation" (and others) but I can't really find much. But anyways... I have ...
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All geometry in computer graphics are transformed by position * transform matrix; The issue is the fact that position is a vector with 3 components (x,y,z); And transform matrix is a 4 by 4 with one ...
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Think of cutting open a cubical box with the smallest possible cuts to lay it flat. A cube has 12 edges and it seems in all the possible meshes, you have to cut along 7 edges. So, the most possible ...
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I have a cuboid in 3D space, it is not regular at all. I do have the coordinates of its 8 vertices and my problem is how to determine a given point coordinate is inside or outside this cuboid. I ...
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I am currently having issues with calculating plane intersection of a ray. I start with the following equation $P = P_0 +tR_t$ $R_t$ is the Unit Vector of the Trajectory. Now we have a plane ...
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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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