Mathematics Stack Exchange
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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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Find 3rd point in 3D space based on position of 2 points

Assuming i have 2 points $P_1$ and $P_2$ having coordinates of $P_1 = (x_1, y_1, z_1)$ $P_2 = (x_2, y_2, z_2)$ I want to find the coordinates of a 3rd point ($P_3$) where it creates a straight line if connected with $P_1$ and $P_2$ P3 should be…
TeAmEr
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slope of a plane

I'm trying to understand the math behind 3d perspective clipping algorithm dixit: We need four constant to express the equations of the four side planes. These are the slopes of the planes in relation to the z-axis. Figure 6.27 shows a vertical…
user2321651
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Vector Rotation in 3D

Given: Two points: ($x_1$, $y_1$, $z_1$), ($x_2$, $y_2$, $z_2$) A vector that is parallel to the $x$-axis and points to ascending numbers (intuitively stated, the vector points 'East'). I am hoping for a formula that tells me how many degrees…
Mark P.
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Intersection of a line on a plane

I have two points $P_1=(x_1,y_1,z_1)$, and $P_2=(x_2,y_2,z_2)$, also I have my plane values $A,B,C $ and $D$ too. I know that $P_1$ lies on a side of the plane, and $P_2$ lies on other side of the plane, so there is an interesection with these two…
user2321651
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equation of a plane through 2 points and parallel to a line

what is the equation of a plane passing through 2 given points (p 1) and (p 2) and parallel to a given line L 1? i know how to find the equation of a plane passing through a point with position vector a and parallel to 2 lines with vectors b…
krazkat
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Centre of the sphere

A variable plane passes through a fixed point $(a,b,c)$ and cuts the coordinate axes at $P,Q,R$. Then the coordinates $(x,y,z)$ of the centre of the sphere passing through $P,Q,R$ and the origin satisfy which of the following equation? (A)…
idpd15
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3d transformation in html5

I am trying to understand 3d-transformation in html5 and when it's rotation, scaling and moving - it is simple. But adding perspective confuses me. For example we have a rectangle: [400, 200], origin is in the center [200, 100], transform matrix…
user2664687
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Finding coordinates of closest approach

Given two lines $l_1=\mathbf E_1+k\mathbf E'_1$ and $l_2=\mathbf E_2+\mu\mathbf E'_2$ in 3D, there exists a shortest distance between the two lines. How does one find the coordinates of the points $P$ on $l_1$ and $Q$ on $l_2$, such that $P$ and $Q$…
user103106
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Find the equation of a plane containing two given points and having a given distance to a third point

This problem is part of examination preparation material for second mid-semester test of 12-th grade in my school: In the 3D space Oxyz, given 3 points $A(1,0,0)$, $B(0,-2,3)$, $C(1,1,1)$. Let $(P)$ be the plane containing $A$, $B$ such that the…
PhanLong
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In three-dimensional space, when the sum of the distances from an unknown point to two known points is constant, what is the trajectory of the point?

The unknown point P (x, y, z) in three-dimensional space is at a constant sum of distances dPA and dPB from two known fixed points A and B, i.e., dPA + dPB = constant. How can we express the trajectory of P? I know that in the two-dimensional plane,…
ZHIHA
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cant find the orthogonal proyection of the line on a plane. plane: 10x-6y-12z=7, line: (8-15t,9t,5+18t).

i have the following: when replacing x,y,z values of the line on the plane equation: 10(8-15t)-6(9t)-12(5+18t)=7, t=13/420.Then if we replace "t" in the equation of the line, we obtain the intersection point (211/28,39/140,389/70). now how do i find…
Julian Navarro
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For a continuous rotation representation in 3D, do you need at least 4 real variables?

I'm pretty sure I have read this somewhere, but I just can't get to find this theorem anywhere. Is there a theorem that states that for a continuous rotation representation you need at least 4 real variables?
ebernardes
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How to convert from world coordinates to camera coordinates

In the world coordinate system, there are objects with rotation values rx1,ry1,rz1 and position values px1,py1,pz1. Similarly, there is an object in the world coordinate system with rotation values rx2,ry2,rz2 and position values px2,py2,pz2. What…
taichi
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The equation of the line parallel to $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ intersecting the lines $9x+y+z+4=0 =5x+y+3z$ & $x+2y-3z-3=0=2x-5y+3z+3$

The equation of the line parallel to $\frac{x}{2} = \frac{y}{3} = \frac{z}{4}$ intersecting the lines $9x + y + z + 4 = 0 = 5x + y + 3z$ & $x + 2y - 3z - 3 = 0 = 2x - 5y + 3z + 3$ is (A) $7x + y + 2z + 2 = 0 = x - 2y + z + 1$ (B) $7x - y + 2z +…
Samar Imam Zaidi
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3D forms of a two variables separated function

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: $$|\Psi (x,t)|^2 = \psi^{\ast}(x)\psi(x) e^{it} e^{-it}$$ $$|\Psi (x,t)|^2 = |\psi (x)|^2$$ For every…
niobium
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