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.
948 questions with no upvoted or accepted answers
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Fitting a tetrahedron through the smallest hole
I'm designing a child's toy consisting of a closed box with a hole on top; a unit tetrahedron must fit through this hole.
What is the smallest possible area of the hole?
Currently my hole is an ...
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Decomposing geodesic tessellations over a sphere into parallelograms
I'm working with some icosahedron-based tessellations of triangles over the surface of a sphere.
Class I and Class II tessellations have a nice property where, cutting along the edges of the ...
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Angles of a known 3d vector
I have a 3d vector r known by its coordinates rx, ry, rz. How can calculate angles Theta and Phi ?
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Does a point quadrilateral form a rect in 3D space?
I have 4 points with x and y coordinate and would like to find out a way to check if given quadrilateral would be a rectangle in 3D space.
I tried a bunch of conditions, but there was always and edge ...
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Analytic caustics for 3D objects
Is it possible to efficiently calculate caustics for a given 3D object, like a torus, or a cube?
To be more precise: let's assume that we have a 3d torus, resting on a 2d plane and a single light ...
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A purely algebraic proof of a regular tetrahedron inequality
One of the comments in Prove that inequality $AM \cdot AN + BM \cdot BN + CM \cdot CN \geq DM \cdot DN$
gives the suggestion for proving the inequality
$$ \sqrt{(x-1)^2 + (y+1)^2 + (z+1)^2}\sqrt{(a-1)^...
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Generating a 3d ribbon from a series of points
I am attempting to generate a 3d ribbon from a set of 3d points. The idea is to generate a realistic ribbon which follows those points.
In its current state, one example looks like this:
In this ...
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Can a laser beam traverse all points of $\{0,1,2\}^3 \subset \mathbb{R}^3$ using $12$ mirrors only if it is emitted from outside the open cube?
Let $G := \{0,1,2\}^3 \subset \mathbb{R}^3$, the $3\times3\times3$ grid consisting of $27$ integer points, be given.
We emit a laser beam (infinitesimally thin, traveling in affine Euclidean $3$-...
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What is the class of shapes with maximum area for a given volume and surface curvature?
If we consider a sphere with volume V and radius R, its surface area is minimal among all shapes of volume V. The radius of curvature of the surface is R at all points.
What shapes will we obtain if ...
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net of oblique cone,why it has a shape like this?
today i was building a right cone for my geometry homework.after building the cone, i started to think what shape the net of an oblique cone (cones with circular base which the axis does not pass ...
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Is this a legit way to visualize complex functions?
I am doing laplace transform in a class and I hate how there seems to be no graphical support when things are transformed to laplace domain i.e. nobody cares what they look like in laplace domain
But ...
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Least Squares Conformal Map Algorithm for UV coordinates
Can someone explain Least Squares Conformal Map in terms using Vertices(Vx,Vy,Vz) and UV coordinates or ST coordinate? I have read the lscm paper but I need it in XYZ value to understand it.
http://...
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3d straightedge and compass
Given a tool that can draw a sphere by given center and a point on it and a surface by given 3 points, is the constructable set of the tool equivalent to the streightedge and compass constructable ...
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Symmetrically $3d$ embeddable graphs with high girth
Let a symmetrically $3d$ embeddable graph be a graph that can be embedded into $3d$ so that the embedding is arc-transitive, which means that every vertex-edge pair with the vertex incident to the ...
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Rotating a 3D shape so that it gets heated evenly by a fire
Imagine you have a shape (say, an eggplant) that you want to cook roughly evenly on a fire. How should you rotate the eggplant to accomplish this?
More concretely, the surface of the eggplant (before ...
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Number of ways to mark the edges of a net of regular tetrahedra
Abstract
This problem originates from Chemistry. You will soon find that the Oxygen and Hydrogen in the image can be replaced with vertices and arrows, which is why I propose it here. Although its ...
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Spinning a convex polyhedron
We all know how easy it is to spin a coin on a table top. With a good twist,
it might spin for 20 seconds or so before wobbling flat.
E.g., YouTube video.
Let's view a coin as a convex polyhedron.
Q. ...
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3
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Interesting tetrahedron problem with right dihedral angles
A tetrahedron WYXZ, which all sides are acute triangles, has right dihedral angles at WY and XZ. Is there a way to prove that the orthocenters of all faces are on one plane?
The way I tried to solve ...
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Detecting topology in 3d space for polygons
I have some points lying on the surface of a sphere with icosahedral symmetry. I have triangulated the surface of the sphere with hexagons and pentagons as shown in the first figure. As an example, ...
user476433
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How to generate variable pitch helix in nurbs form
I would like to define a helix with a
start pitch
end pitch
start radius
end radius
start angle
The pitch and radius parameters should be interpolated linearly from each end along the length of the ...
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How can i reflect position and direction vectors from a plane
I'm now working on a project that has mirrors. I'd like to reflect a virtual camera and the way which i can do this is to reflect two vectors - position and normalized direction vectors of the camera. ...
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What function has a 3D graph that will look like a spiral into a singularity?
I am trying to draw text spiraling into a black hole, from a more interesting slightly off-orthogonal viewpoint.
I think a function that defines a black hole/singularity surface might look something ...
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Proving the 3-d pythagorean theorem on surface areas of oblique triangular pyramid
I would like suggestions if possible, other than the really sloppy picture, I'll edit that once my dad gets me Microsoft office. I got a snip of the shape, and edited it as best as I could.
The ...
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Why does aliasing cause loss of a degree of freedom in Euler angles?
I'm reading a book on 3D game math where the author points out that when using Euler angles the same orientation can be reached by doing two different operations; say rotating a cube 90 degrees around ...
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Convolution theorem in 3D
Suppose to have a 3-dimensional discrete grid. I would like to convolve it with a 3-dimensional tensor (a 3x3x3 "cube"), applying the convolution theorem. Hence, I should apply a Fourier transform to ...
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