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.

3724 questions
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General equation of sphere through a plane and a circle

Given the equation of circle $x^{2} + y^{2} = a^{2}$ and the equation of the plane $z=0$ Why is the general equation of sphere through them written as $x^{2} + y^{2} + z^{2} - a^{2} + \lambda(z) = 0$ From where does the term $z^{2}$ comes in the…
user1611542
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Formula For 3D Dilation?

If I have a sphere on a 3D grid with it's center being at the origin, and I want to double the size of the sphere, where would it's poles be?
user350058
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Finding a x-y-z equation based on data

I have a large number of x, y, z point values. I am wanting to know the equation that represents these values I have in hand. This equation I am looking for should be a fit that will represent these data points. Which method(s) may I use in order…
Story Maths
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Distance between a point and a 3D figure

If I have some basic 3D shapes like rectangular prisms, cylinders and spheres (whose positions, orientations and dimensions are fully known), what is the simplest way of finding the shortest distance from any given point (x,y,z) to each of these…
Ali250
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Cone in three dimension

According to me the following statements are true Statement 1: The guiding curve of a right circular cone is always a circle. Statement 2: If the guiding curve is a circle then the cone may or may not be right circular. Am I right?
user3575652
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Retrieve Cubes that Share a Vertex

Suppose that we have a world with an infinite number of cubes, each of which are 1x1x1 in size and have integral coordinates, e.g. (1, 2, 3) Given that C is a cube at (XC, YC, ZC) and that P is a vertex of that cube with coordinates (XP, YP, ZP),…
Lucien
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Find the equations of $x-y$, $x-z$ and $z-y$ planes.

Do the $y-x$ and $x-y$ planes have the same equations? I think that the equation of the $x-y$ plane can be $x+y+z=0$ or $x+y+z=4$ or $ax+by+cz=$ any real number and $a,b,c$ are arbitrary real numbers. Am I wrong?
Hunzilas
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finding pixel coordinates

I'm trying to calculate pixel coordinates of 3d points Xw = [150 200 350] where R is given as \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} K is give as \begin{bmatrix} -70\\ -95\\ …
user3273345
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How to function fit a plane through a collection with points with minimal square root of error

I'm working on a computer program that has to stabilize a set of points which should all appear on a plane in 3D space. Currently the program does not use the knowledge that all points should appear on a plane. So I want to write a program that…
Thijser
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Perpendicular Lines.

If two lines $L_1$ and $L_2$ in space, are defined by: $$L_1=\{x=\sqrt{\lambda}y+(\sqrt{\lambda}-1)\\z=(\sqrt{\lambda}-1)y+\sqrt{\lambda}\}\text{ and }\\L_2=\{x=\sqrt{\mu}y+(1-\sqrt{\mu})\\z=(1-\sqrt{\mu})y+\sqrt{\mu}\}$$ then $L_1$ is perpendicular…
RE60K
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Find an equation of a plane

Find an equation of a plane which contains the points: $(0,0,3),(3,2,1)0$, and $(6,2,0)$ I know I need a vector in order to use the equation $d=ax_0$+b$y_0$+c$z_0$ Now, could I just select any two points as my terminal and initial, say, (0,0,3) and…
Overclock
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Give parametric equations for the line in 3 space

Give parametric equations for the line in 3 space which goes through the point (1,2,3) and is parallel to the line given by the symmetric equations: (x-1)/-1 = (y-2)/3 = (z-2)/1 So, based off those symmetric equations I used the definition of a…
Overclock
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Randomly distribute objects over a surface with some clusters

I want to randomly distribute some(in thousands) objects over a surface. This I can achieve with a function say x,y = rand(). This will evenly distribute objects over the surface, but is it possible to have some control over the randomness like…
Bhupen
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Line of greatest slope

Assuming the plane $4x-3y+7z=0$ to be horizontal, find the equation of the line of greatest slope through the point $(2,1,1)$ in the plane $2x+y-5z=0$
Pratyush
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Finding the length from a point to a line in 3D??

Here is the question: What is the distance from the point $(4,1,-2)$ to the line given by : $$x=2+t$$ $$y=3+3t$$ $$z=4-t$$ Help would be greatly appreciate, as i do not even understand where to start. I am having a hard time understanding this…
JoshBoiskin
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