The (3d) tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For geometry that is not on a plane, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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2answers
99 views

Projecting 3D Point to Plane

I have a plane defined by the equation $Ax + By + Cz + D = 0$. It does not pass through the origin. I have projected the origin of my global coordinate system onto the plane, so it is at $(a, b, c)$. ...
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1answer
69 views

the surface area of the cream white colored surface wants to be calculated using integral

I Want to calculate the area of the cream colored surface illustrated on the image below using integral. variables are $\beta$ and $\phi$ and constants are R and r
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2answers
46 views

What is the difference between $z=0$ plane and $26z=0$ plane

I'm using this site to calculate a plane equation. The points are $(2,3,0)$, $(5,1,0)$ and $(6,9,0)$. The result is $26z = 0$ plane. Is there a difference between $26z =0$ and $z = 0$? Moreover, ...
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0answers
113 views

Map points between 3D Coordinate systems

I am trying to find a way to relate two 3D coordinate systems. I have 24 points for each system and found this, but it only works for 2D coordinate systems: ...
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2answers
135 views

How to rotate a plane in 3-D using standard form?

I have a set of points $N = \{n_1, n_2, ...\}$ on a plane $z = 0$. And I have another set of points $M = \{m_1, m_2, ...\}$ on plane $ax + by + cz + d = 0$. $|N| = |M|$ $\forall n_i, n_j \in N$ and ...
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1answer
306 views

number of planes possible such that it is equidistant from 4 non coplanar points

If there are for non coplanar points find the number of planes such that all four of them are equidistant from the plane . Sorry one of those problems where dont know what to do . How should i do this ...
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1answer
185 views

Finding the missing coordinate of a point within a 3D triangle

We have an equilateral triangle $ABC$ in 3-dimensional space. The points are known, such as: $A = (x_1,y_1,z_1)$ $B = (x_2,y_2,z_2)$ $C = (x_3,y_3,z_3)$ Point $P$ is on triangle $ABC$. If I know ...
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1answer
34 views

Vectors to Matrices in algebraic equations

This question is based off of Dave Eberly's 3D Game Engine Design, 2nd Edition. I am reading it slowly to gain a larger algebraic grasp of 3D graphics, which this book seems to offer. When finding a ...
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2answers
171 views

Calculating Intersection of Three Spheres Step by Step

How do I calculate the intersection of three spheres step by step? Assume that the spheres are $S_i(c_i, r_i)$ where $i = 1,2,3$, $c_i$ is the center coordinates of $S_i$ and $r_i$ is the radius of ...
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1answer
52 views

Equation of a plane passing through a point

Write an equation of the plane with normal vector n=<-6, 9, -8> passing through the point (-1, 3, 4) in scalar form. The equation should equal 2. I just learned this topic and I am having ...
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2answers
29 views

Plane in 3 Dimensions

I just learned this topic and I'm having trouble with this homework problem... Find an equation of the plane through the three points given: $P = (0, 2, 0)$ $Q = (-4, 6, 2)$ $R = (3, 3, -1)$ The ...
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2answers
137 views

Unreliable algorithm for determine if points lie along a line?

So lets say I have some points $A,B,C$. A method I have been shown for determining if the lie along a straight line is thus: $\mathrm{If}\space|AC|=|AB|+|BC| \space\mathrm{then\space A,B\space ...
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0answers
327 views

Transform a vector to global frame and ignore rotation about one axis or Full tilt compensated magnetometer

Good day everyone. I would like to lock the rotation about one specified axis. For example, let`s imagine that we have a quaternion which desribes the orientation of our rigid body relative to the ...
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0answers
508 views

Function of an object that has a shape of circle, square and triangle on 3d projection

What is the function of this kind of object (solid on the bottom right)? I got a lot of material for pondering with keyword cylindrical wedge and hoof, but this is something inverse compared to it. ...
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1answer
125 views

How do I calculate the dimensions of this Frustum?

So, I saw this question in a book, You have been given a cone. The cone's base angles are both equal to 75° and the vertical angle is (of course) 30°.The radius of the cone is 7 metres.Now, ...
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1answer
60 views

Rays in the space

I have a nice problem from a mathematical circle: Let n be a positive integer. Determine the smallest n with the property in the space having
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1answer
349 views

Ellipsoid intersection

Let $E$ be an ellipsoid centered at $p = (x,y,z) \in \mathbb{R}^3$ and let $T:\mathbb{R}^3 \to \mathbb{R}^3 $ be a linear transformation which transforms $E$ to a unit sphere. Let $R$ be the ray $p_0 ...
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2answers
85 views

Rotate $z = 0$ plane in 3D

I have 100 points on $z=0$ plane. I want to rotate those points, such that they lie on any plane $P(a,b,c,d)$, preserving distances. Hence, I need a rotation matrix. For instance, if my points are ...
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1answer
66 views

Distortion in spherical coordinates

I'm trying to realized 3d models of stones. My idea was to create a 2D random angular distribution with opportune correlation, namely $R(\theta,\varphi)=rand(\theta,\varphi,c_l)$ where ...
2
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1answer
41 views

is there a higher dimensional analogue of the first isogonic center?

I'm curious to know if, given four points $a, b, c, d$, you can always find a point $p$ such that last lines $pa, pb, pc, pd$ form equal angles pairwise. I'd also appreciate resources on 3d geometry ...
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0answers
43 views

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 ...
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0answers
53 views

Collision of two moving lines (3D)

I have two lines / edges moving with linear velocity in timesteps. How do I determine whether the lines collide / intersect in the intervening period? My lines are (P1,Q1) and (P2,Q2). The endpoints ...
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1answer
112 views

Calculation of an average plane without using a covariance matrix

I need to calculate the normal to an average plane using the positions of >3 points (for 3 points, I know how to do it with a cross-product). My main problem is that it needs to be a simple method ...
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1answer
31 views

Vectors In Three Dimensions

Hi! I am working on some online homework for my calc2 class and I am having trouble with this problem. I first set $r_1$ and $r_2$ equal to one another to get $(-1-4t, 2+2t, -14+2t)=(-13+4t, 8-2t, ...
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0answers
99 views

Rotation rate around one axis transformed to a different axis at an angle to the first

Suppose I have a motor with axis M on my diagram rotating at rate $r$ [rad/sec]. Connected to the motor is a gyroscope, the axis G of which is at an angle a to to that of the motor (the gyroscope ...
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1answer
372 views

Find normal vector of circle in 3D space given circle size and a single perspective

I don't really know what to search up to answer my question. I tried such things as "ellipse matching" and "3d circle orientation" (and others) but I can't really find much. But anyways... I have ...
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0answers
31 views

How do I do the math necessary to make these five matrices multiplied together equal the result shown?

I'm currently studying the math involved with rotating vertices around an arbitrary axis in 3D space. For this, I have found the following page to be very helpful: ...
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1answer
327 views

Volume between paraboloid and plane

I need to find the volume of the finite region enclosed between the surface $$ y = 1 - x^2 - 4z^2 $$ and the plane $$y = 0$$ Here's what I've done: $$ \int\int ...
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2answers
511 views

Finding a normal to an ellipsoid

Let $E$ be an ellipsoid centered at $v = (x,y,z) \in \mathbb{R}^3$ and let $T:\mathbb{R}^3 \to \mathbb{R}^3 $ be a linear transformation which transforms $E$ to a sphere $S$ with a radius of length ...
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1answer
49 views

Converting 3D into 2D

I have a quad and I'm trying to convert its vertices so that they're facing the camera which is lying at 0,0,1 looking down the Z, or not even specifically facing the camera, just so they're facing up ...
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1answer
24 views

Find close-enough points in 3d space

I have 2 sets of points in 3d space , each set of size n. I need to calc. all the points from the first set the are close enough (dist between 2 points < TH, TH is given) to at least one of the ...
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1answer
151 views

Collinear points in 3dimension

Given three $3D$ points: $A,B$ and $C$, what is the procedure to check if they are collinear? In general, given $n$ points in $m$-dimension, how should one find out, if these $n$-points defines a ...
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2answers
79 views

Unusual 3D Packing Problem

I made up this interesting problem playing with wire sculptures: If I have a $10 \times 10 \times 10$ clear box and inside I can put wireframe unit cubes, what's the maximum number of unit edges (or ...
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1answer
187 views

How to draw contour lines (projections) on axis x or y with octave?

With the builtin function contour(x,y,z) of octave one can draw level curves where z remains constant. My question is how to draw contour lines on axis x or axis ...
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1answer
152 views

How to draw arrows by rotating lines in 3d space?

I am trying to figure out direction vectors of the arrowheads of an arrow. Basically I'm given a normalized direction vector ...
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1answer
55 views

How do I multiple these matrices together?

As a personal brain exercise, I've recently been trying to work out the math involved with rotating vertices around an arbitrary axis in 3D space. To do so, I've been relying very heavily on the ...
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1answer
39 views

Find the normal of a polygon with vertices that are not linearly independent in 3d

For example, take the vectors: $(1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15)$ What would the normal to the polygon be? I'm guessing it would be $(0,0,0)$? For vertices that are linearly ...
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1answer
267 views

Counting the number of cubes in an isometric view

I had seen questions in a sample aptitude test, where an isometric view of an object made up of cubes was given, with some of the cubes removed. We were supposed to count the number of cubes present ...
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1answer
1k views

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 ...
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1answer
37 views

Determine if a point is within two planes [closed]

I have a point P and two planes defined by three vertex each. How can I determine if P is between the two planes?
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1answer
315 views

Finding the coordinates of a point on a line that produces the shortest distance to another point in 3 dimensions.

I have a question with two parts and it looks like the following: a) Determine the distance from point $A(-2, 1, 1)$ to the line with the equation $\vec{r} = (3, 0, -1) + t(1, 1, 2)$, $t\in \Bbb R$ ...
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2answers
44 views

How do I calculate the inverse of these matrices?

In learning how to rotate vertices about an arbitrary axis in 3D space, I came across the following matrices, which I need to calculate the inverse of to properly "undo" any rotation caused by them: ...
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2answers
43 views

Finding an equation of a plane a certain distance from a given plane

I just wanted to know the methodology of how to solve for the equation of a plane that is some distance from some given plane. Thanks. Any help is appreciated
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5answers
278 views

Is the rhombic dodecahedron the only isohedral polyhedron that tiles 3-space (other than the cube)?

Is the rhombic dodecahedron the only face-transitive (or isohedral, i.e. all faces are the same) polyhedron that seamlessly tiles 3-dimensional Euclidean space (other than the cube)? I'm looking ...
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1answer
139 views

rotation matrix to axis angle

from wikipedia the above rotation matrix has a rotation of -74 degrees. What does it mean "around the axis (−1⁄3,2⁄3,2⁄3)"? How can I determine how many degrees is rotated on X axis, Y axis and Z ...
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1answer
23 views

Make a point orbit another point, given time and a normal.

I am working in 3D space. I am trying to make a solar system model. known variables: center of orbit, C (x,y,z) normal, perpendicular to the orbit, N (x,y,z) radius of orbit, R time, position ...
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2answers
47 views

Local max/min points, partial derivatives

I'm having a lot of problems with figuring out how to properly do max/min with partial derivatives. To my knowledge, we have: $$D(x, y) = f_{xx}(x, y)f_{yy}(x, y) - (f_{xy}(x, y))^{2}$$ With the ...
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2answers
65 views

How to find a normal vector from an equation in the form f(x,y)?

If I have an equation $f(x,y)$ which given the $x$ and $y$ coordinate, it gives you the $z$ coordinate. How can I find the normal (directional) vector of the the point $(x,y,f(x,y))$? This would be ...
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1answer
402 views

Finding the counter-clockwise direction of points in 3d

I have a set of 5 points of a polygon in 3d. I want to order these points in a counter-clockwise direction. How do I do this? In 2d, to check if two points are ordered counter-clockwise or ...
2
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1answer
289 views

Incenter of Triangle in 3D

I'm trying to figure out how to find the incenter of a triangle with (x, y, z) coordinates for the verteces. I can find the lengths of the sides and the radius of the incircle from that, so I've ...