Mathematics Stack Exchange
Mathematics Stack Exchange

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.

3838 questions
200
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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 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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151
votes
15 answers

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
  • 10,045
110
votes
8 answers

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
  • 24,817
62
votes
11 answers

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
  • 653
45
votes
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
  • 451
43
votes
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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39
votes
4 answers

What is the shape of the perfect coffee cup for heat retention assuming coffee is being drunk at a constant rate?

Find the optimal shape of a coffee cup for heat retention. Assuming A constant coffee flow rate out of the cup. All surfaces radiate heat equally, i.e. liquid surface, bottom of cup and sides of cup. The coffee is drunk quickly enough that the…
Michael McLaughlin
  • 598
38
votes
2 answers

Hexagons are best for tiling 2D space in terms of perimeter vs area. What's best for 3D space?

If you think of the bee-hive problem, you want to make 2D cells that divide the plane of honey into chunks of area while expending the least perimeter (since the perimeter of the cells is what takes up resources/effort). The solution ends up being…
chausies
  • 2,438
37
votes
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
  • 1,471
35
votes
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
  • 10,280
35
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2 answers

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
  • 453
29
votes
9 answers

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.
  • 473
27
votes
5 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
  • 6,408
27
votes
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…
Rory McEwan
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25
votes
1 answer

3D projection on a 2D plane ( weak maths ressources )

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' axes ( The (OXY) plane is the same as the (OX'Y')…
Put Me
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