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.

This tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead . For non-planar geometry, but otherwise agnostic of dimensions, perhaps or should also be considered.

Learn more about 3-dimensional space here.

3304 questions
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Calculate Rotation Matrix to align Vector A to Vector B in 3d?

I have one triangle in 3d space that I am tracking in a simulation. Between time steps I have the the previous normal of the triangle and the current normal of the triangle along with both the current and previous 3d vertex positions of the…
user1084113
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Why is the volume of a cone one third of the volume of a cylinder?

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 considering a cone as a solid of revolution, but I would…
bryn
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78
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What is the equation for a 3D line?

Just like we have the equation $y=mx+b$ for $\mathbb{R}^{2}$, what would be a equation for $\mathbb{R}^{3}$? Thanks.
Ovi
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How to calculate the area of a 3D triangle?

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. (119.91227722167969, 122.7717056274414, 39.3568115234375),…
iamgopal
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42
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4 answers

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?
Simon Verbeke
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38
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6 answers

Parametric Equation of a Circle in 3D Space?

So, my dilemma here is... I have an axis. This axis is given to me in the format of the slope of the axis in the x,y and z axes. I need to come up with a parametric equation of a circle. This circle needs to have an axis of rotation at the given…
iAndr0idOs
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35
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3 answers

Will 3 lights illuminate any convex solid?

Can 3 lights be placed on the outside of any convex N dimensional solid so that all points on its surface are illuminated?
Angela Pretorius
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31
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slope of a line in 3D coordinate system

Suppose I have $2$ points in a 3D coordinate space. Say $p_1=(5,5,5)$, $p_2=(1,2,3)$. How do I find the slope of the line joining $p_1$ and $p_2$? After getting the slope (which I assume will be an integer) how do I get the coordinates of any…
2am
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31
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4 answers

uniform random point in triangle in 3D

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 convex combination of the vertices: $P = (1 -…
dsg
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29
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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 terrific if this program could also compute and…
Andrew S.
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27
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4 answers

Are there any paths that will always show if there is a limit?

I'm trying to do limits in 3D and I'm wondering whether or not there are paths along which the limit of any function at any point can always be found. In my book it isn't clear whether this exists or not; neither is it clear how to choose a path if…
calcstudent
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22
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2 answers

Understanding the Equation of a Möbius Strip

I am in HL Math and trying to finish my IA. My topic is the Möbius band. The only problem is, I do not understand the formula that defines it and everywhere I have looked has just given me a math-jargon filled explanation of parametric equations…
Emily
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21
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3 answers

Formula to project a vector onto a plane

I have a reference plane formed by $3$ points in $\mathbb{R}^3$ – $A, B$ and $C$. I have a $4$th point, $D$. I would like to project the vector $\vec{BD}$ onto the reference plane as well as project vector $\vec{BD}$ onto the plane orthogonal to the…
MsHF
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21
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6 answers

Composition of two axis-angle rotations

Please note that I am not referring to Euler angles of the form (α,β,γ). I am referring to the axis-angle representation, in which a unit vector indicates the direction axis of a rotation and a scalar the magnitude of the rotation. Let…
user76284
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20
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7 answers

Rotating one 3d-vector to another

I have written an algorithm for solving the following problem: Given two 3d-vectors, say: $a,b$, find rotation of $a$ so that its orientation matches $b$. However, I am not sure if the following algorithm works in all cases: 1) Find axis and angle…
Libor
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