# 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.

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### How to calculate the 3-D area of a n-ogon?

Let n = # vertices represented by [x,y,z] coordinates. Apply, the general formula to the coordinates below letting n = 5 Where the points are: [13.28, -14.6, 90.35] [0.16, 8.12, 81.12] [-1.75, 8.35, ...
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### Finding the inverse of an $xyz$ Euler transform. [closed]

So I am trying to find the inverse rotation for the Euler $xyz$ rotation $(-0.4,-0.5,-1.0)$. I actually need this for Blender ($3D$ software) (In the geometry nodes for those who know!) Blender ...
1 vote
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### Tangent Space View Direction based factor value remap

I'm trying to setup a mask similar to what Fresnel produces. Unfortunately Fresnel gives pretty bad results at grazing angles so I ended up using this : ...
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### Need help in quantitatively modeling solubility of carbon dioxide in beer.

I'm trying to model a 3D surface which reflects the solubility of $CO_2$ in beer. An empirically derived chart is available at this link. Solubility is empirically related to the pressure of $CO_2$ in ...
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### How to rotate an object in-place along an arbitrary axis in three dimenstions

Consider the following cube floating in 3D space. How do I rotate it in-place along the axis specified by the vector $\vec{V}$? I know how to rotate a point about an arbitrary axis, but it doesn't ...
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### Calculating the volume of an arbitrary mesh

Given a mesh (vertices, edges, faces), I need to calculate the volume of the formed mesh. By volume, I mean the amount of space that a substance or object occupies. The resulting volume does not ...
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### Determine equation of plane that intersects an ellipsoid which results in a specified eccentricity of the resulting intersection ellipse

Suppose you're given the ellipse $$\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} + \dfrac{z^2}{c^2} = 1$$ I would like to find the direction of the normal to the cutting plane to this ellipsoid that will ...
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1 vote
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### Calculate remaining filament based on rotation

This might not be possible at all but I can't get my head around it, not really mathematically minded. A 3D printer spool obviously depletes as it is used. Knowing the diameter of the filament, the ...
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### Why is the sum of cosines of angles defining a point [duplicate]

Consider a point P in 3D space which makes an angle $\alpha$ to the $x$-axis an angle $\beta$ to the $y$-axis and an angle $\gamma$ to the $z$-axis. The sum of the squares of the cosines of these ...
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### Restoring third coordinate for triangle by its orthogonal projection and similar triangle

Suppose we have triangle $\Delta OAB$ lying on plane $z=0$ with coordinates $O(0,0,0), A(x_a,y_a,0), B(x_b,y_b,0)$ Also there is triangle $\Delta EFG$, but we know only coordinates of its orthogonal ...
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1 vote
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### Locus of middle points of the chords of conicoid which are parallel to $xy$ plane and touch the given sphere

I have the following conicoid before me: $ax^2+by^2+cz^2=1$ I have to find the locus of the middle points of the chords which are parallel to the plane $z=0$ and touch the sphere $x^2+y^2+z^2=a^2$. ...
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### how to offset a rotation contained in a unit quaternion rotation from the origin of a rigid object.

I'm using Unity3D for a project. The way it handles sorting transformations is with a 3vector-unit quaternion-3vector "sandwich" (the 1st vector for position, the quaternion for rotation, ...
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### Identify the intersection between a Quadric and a plane

I am considering a given quadric $r^T Q r + b^T r + c = 0$ and its intersection with a given plane $n^T (r - r_0) = 0$ and I want to identify the intersection curve between the two. My attempt: ...
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1 vote
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### Hyperbola dimensions - intersections cone and plane

I’d like some help to understand how to derive the relationship of the intersection of a cone with a plane parallel to the cone axis. See below dimensions of the shapes involved. What I want to ...
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### Calculate normal vectors for each element of a grid in Python

How can I quickly calculate the normal vectors of each mesh of my grid? (grid is defined by the three matrices Mx, My & <...
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### Volume of a triangular prism with 2 different bases

How do I arrive at a formula to calculate the volume of the following 3D shape? Does this shape have a proper name? It kind of looks like an irregular triangular prism with 2 similar triangles as ...
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My question is simple: how do you add a shadow effect (like the one in Kalles Fraktaler 2)? I have tried distance estimation, but have failed at creating it reliably. I would like a relatively fast ...
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### How many distinct ways to flatten a cube?

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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### What does a flattened Teserract look like?

This question is best asked with a picture: In words, we can flatten a cube into 2-d space and get a set of flattened squares like in the top right of the picture where five of the edges have stayed ...
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1 vote
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### Practical geometry problem: Maximum dimensions of a box that can be moved down a particular flight of stairs that make a U-turn

I really hope you can help me out with a (hopefully basic) very practical problem. I've bought a two floor house. The first floor is connected to the second with a double flies of stairs that make a U-...
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### Finding the vertex of the parabola parameterized by $p(t)=P_0+P_1t+P_2t^2$ for vectors $P_0, P_1, P_2$

A parabola can always be described in parametric form by position vector $p(t)$, $p(t) = P_0 + P_1 t + P_2 t^2$ where $P_0, P_1, P_2$ are vectors in $2D$ or $3D$. I would like to prove that the ...
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### Given two points$P_{1}(0, 0, 0)$ and $P_{2}(2, 2, 0)$ what is the plane equation equidistant from $P_1$ and $P_2$? [closed]
I have given two points $P_{1}(0, 0, 0)$ and $P_{2}(2, 2, 0)$ what is the plane equation equidistant from $P_1$ and $P_2$? How can I find this?
I am looking for all the possible forms in 3D space of the function defined as $$\Psi(x,t) = \psi(x) e^{-it}$$ There is this funny constraint: $$|\Psi (x,t)|^2 = \psi^{\ast}(x)\psi(x) e^{it} e^{-it}$$...