# Tagged Questions

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### How To Find a Set of Points Farthest Apart Within 3D Solid

I am trying to find out a method to solve the following problem: There are two parameters: 1) There is a solid 3D region plotted in a cartesian coordinate system. 2) There is a number of points that ...
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### Volume of Cavity between intersecting multiple Spheres

I want find an equation for this problem: Problem Statement:: I have different size sphere, for example say $R_1$ for Red balls and $R_{2}$ for white Balls, overlapping each other. 1.) I want to ...
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### Intersection of a plane and a surface of revolution

I'm am stuck on the following problem: I have the equation of a curve in the plane $(x,z)$: $z=f(x)$. I build a surface of revolution in the space rotating this curve around the $z$ axis. I need to ...
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### Difference between polyhedral, CSG and B-rep

I am working on the 3D object modeling project. I found objects can be represented in the form of Polyhedrol model, CSG (Constructive Solid Geometry) model, and as well as B-Rep (Boundary ...
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### Ellipse Tangents in 3D

I know that we can find the tangent of the ellipse in 2D by taking the derivative of the equation defining the ellipse. But I'm little bit confused about finding the ellipse tangent in 3D. Where the ...
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### vectors in 3D space and Right-Hand Rule

Suppose we have three vectors in 3D space. My questions are: How we check if these vectors are satisfy the right-hand rule or not. I know that it's possible to make the three vectors satisfy the ...
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### The exact type of my 3d model

I have reconstructed vertical features (hole like objects lie on a vertical face) lie on two connected faces. To understand the situation, I say I have 2 walls with many windows and doors on ...
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### Perspective projection onto y/z plane?

On wikipedia there is an article on 3d perspective projection onto the x/y plane. http://en.wikipedia.org/wiki/3D_projection#Perspective_projection How do I project onto the y/z plane? If i have a ...
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### Which solids are characterized by their orthographic projections?

If I know the orthographic projections of a given solid in Euclidean 3-space onto the $xy$, $xz$ and $yz$ planes, under which circumstances can I reconstruct the solid based on that information alone? ...
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### Eigenvectors for the equation of the second degree and right-hand rule

I'm trying to find the Eigenvectors for the equation of the second degree (for example Elliptic cone). The estimated values $V_1$, $V_2$ and $V_3$ must satisfy the right-hand rule. How can we verify ...
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### get a rotation matrix from an oriented vector quicker than Euler

I'm in $R^3$ and I have a solid 3d object and a vector, I would like to rotate and orient the solid according to this vector. I found that the simplest way to do that is to use euler angles, the ...
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### Maximum length of pencil in a pencil case

What is the maximum length of an unsharpened, cylindrical pencil inside an empty rectangular pencil box? Or, in a rectangular cuboid of dimensions $x \times y \times z$, what is the maximum possible ...
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### What is the formula for a 3D line?

Just like we have the formula $y=mx+b$ for $\mathbb{R}^{2}$, what would be a formula for $\mathbb{R}^{3}$? Thanks.
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### Surface of Cone

A cone is cut by a plane ($z=d$). ($0<d<c$) The top point of the cone is $A(a,b,c)$ Button of the Cone is a circle on $z=0$ plane and center of it is $O(0,0,0)$. If $a=b=0$ then ...
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### To find the volume of tetrahedron by using all surfaces areas?

I am looking for a formula: $V=f(S_1,S_2,S_3,S_4)$, where $S_1$, $S_2$, $S_3$, and $S_4$ are the areas of the four faces. We know ...
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### will 3 lights illuminate 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?
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### Overlap volume of three spheres

Given three spheres and their coordinates with equal radii that are known to have a triple overlap (a volume contained within all three spheres), is there a known closed form for the calculation of ...