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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0answers
9 views

Non-standard 3D rotation of a set of points

I want to create a 3D surface as shown in the figure below. Toward this, I thought if I rotate a set of points in $xy$-plane on a elliptical arc I may be able to get such a surface. I was thinking of ...
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1answer
26 views

Calculate the viewing-angle on a square (3d-calc)

I'm in big trouble: My program (Java) successfully recognised a square drawn on a paper (by its 4 edges). Now I need to calculate, under which angle the webcam is facing this square. So I get the 4 ...
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1answer
16 views

Determine similarity between two sequence of quaternions while allowing a degree of freedom around Z axis

A person holds his phone and rotates it in space in a sequence. I am able to obtain a sequence of quaternions from the phone's motion sensors representing the rotation of the phone from the phone ...
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5answers
301 views

Relation between edgelengths in a tetrahedron with two right angles and three equal edges

I have got a problem I can't solve myself. I had an attempt, but it's wrong. I was told to draw a grid of this tetrahedron and then it's easier to find a solution (I tried it, but I don't see ...
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0answers
25 views

Determine Euler Angles from look, up, and cross vectors

I have a spaceship flying through a $3D$ space. The flight is determined by applying a quaternion to the look, up, and cross vectors with the following scheme (this is working perfectly): starting ...
2
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0answers
28 views

Creating an ellipsoidal 3D surface

I am trying to find the equation of a 3D ellipsoidal surface. I have thought of two approaches which are schematically shown below: By revolving an elliptical arc over a 3D elliptical path: Or by ...
3
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2answers
1k views

Form a Parallelogram by 4 Points

This is a question from my school. The following is the whole question. The vertices of a triangle $A$, $B$ and $C$ are given by the points $(-1, 0, 2)$, $(0, 1, 0)$, $(1, -1, 0)$ respectively. ...
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4answers
5k views

Calculate distance in 3D space

Imagine I want to determine the distance between points 0,0,0 and 1,2,3. How is this calculated?
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1answer
318 views

Intersection of a line segment and a paraboloid in 3D

Suppose I have a line segment $L$ in 3D: $$x=a_1(1-t)+b_1t$$ $$y=a_2(1-t)+b_2t$$ $$z=(a_1^2+a_2^2-k_1^2)(1-t)+(b_1^2+b_2^2-k_2^2)t$$ Because $L$ is line segment then $0\leq t\leq 1$. And defining ...
3
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1answer
267 views

3D Rotation Decomposition?

I have a 3D local xyz coordinate system placed in a world ENU (East-North-Up) coordinate system. The current relationship ...
2
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3answers
1k views

How to show two points in $\mathbb{R}^3$ form a plane and determine equation?

Given two arbitrary equidistant points in $\mathbb{R}^3$, ($p$ and $q$), how would one show that they form a plane and what would the equation of that plane be? Defining two vectors in ...
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1answer
26 views

Volume of a cylinder cut by a plane

I've looked online but I can't seem to find a calculus proof for the volume of a cylinder cut by a plane. The question is:...
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3answers
21k views

how to calculate area of 3D triangle?

I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. ...
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0answers
31 views

Slope of image side for 3D rotation

I had a new idea for an experimental 3D assembler (not a rasterizer). The idea requires that I get the slope of the top, bottom, left, or right depending on the $z_n$ axis. My idea works on two ...
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0answers
24 views

Find 3D concave hull based on original model and convex hull

I want to find the concave hull of a 3d model, with a threshold for the maximum edge size. Googling around let me to the following approach (mainly abstracting from 2d approaches): Determine the ...
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1answer
31 views

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 $2x+y-5z=0$
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1answer
167 views

Getting a 3d linear equation knowing the rotation of an object

I have an object, a simple rectangle I rotate it by a certain degree using Euler Angles, in this case around Z, to make it easy lets say it's 45 degrees. Right now I want the yellow: Y-Axis linear ...
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1answer
351 views

Equation of plane through intersection of planes and parallel to line

Find the equation of the plane through the intersection of the planes of $x-2y+z=1$ and $2x+y+z=8$ and parallel to the line: $\frac{x-3}{1} = \frac{y-1}{2} = \frac{z-2}{1} $ I'm facing difficulties ...
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1answer
18 views

Intersection point in a 3D figure

I was considering the maximum number of points in a 3D-figure such that all the internal line segments of the figure (all the lines that have endpoints as vertices of the figure, and go through the ...
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0answers
25 views

How to create cube in 3d with given center , height vector , width vector and depht vector?

I want to create cube in 3d. I have center point of cube, height vector , width vector and depth vector. using this information i want to create vector. e.g. Center point = (1, 5, 7) Height Vector = ...
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0answers
11 views

Smooth decrease in size when using the dimensions of a cube

I wrote a maze like script a while back, and added in a part which would decrease the size in a linear fashion, based on the percentage of completion. The idea was it'd provide a smooth transition ...
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0answers
14 views

Specific function

I'm looking for a functions with 2 parameters (to plot in 3D) which will satisfy the following criteria: ...
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0answers
15 views

What's the intersection between a cube and a circle inside it and not intersecting its faces? [closed]

What's the intersection of a cube and a circle inside it? is it? 1) the set of point of the circle 2) empty set of points 3) the set of points of the surface of the circle 4) Both 1 and 3
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0answers
13 views

Are the diagonals of cube subset of it?

The intersection of a cube and one of its diagonals is what? 1) This diagonal 2) two of its vertices
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1answer
615 views

Determine if projection of 3D point onto plane is within a triangle

In 3D, given three points $P_1$, $P_2$, and $P_3$ spanning a non-degenerate triangle $T$. How to determine if the projection of a point $P$ onto the plane of $T$ lies within $T$?
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1answer
34 views

When doing 3D rotations my angle flips 180 degrees

I'm implementing 3D rotations for a set of 3D circles. To do that I'm using the parametric equation as described in http://demonstrations.wolfram.com/ParametricEquationOfACircleIn3D/. It works as ...
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1answer
82 views

Incorrect angle detected between two planes

I want to calculate the angle between 2 planes, Reference plane and Plane1. When I feed the X,Y,Z co-ordinates of pointCloud to the function plane_fit.m (by Kevin Mattheus Moerman), I get the output ...
12
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1answer
200 views

Every three of $n$ points is the vertices of an isosceles triangle. What is the max of $n$?

Suppose that we have $n\ (\ge 3)$ points in the three dimensional space and that every three of the $n$ points is the vertices of an isosceles triangle. Here, suppose that the vertices of an isosceles ...
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0answers
23 views

Change of co-ordinate frame

Hi Can someone help me with this question. Say point P and u, v, w are three orthogonal-normalized vectors whose co-ordinate are: P = [Xp, Yp, Zp], u = [Xu, Yu, Zu], v = [Xv, Yv, Zv] and w = [Xw, Yw, ...
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2answers
27 views

How to interpret the equation of a line in 3D through two points, when there are $0$s in the denominator? [closed]

If $A=(0,0,0)$ and $B=(1,0,0)$ are two points of a line in three dimensions, I think its equation should be $$\frac{x-0}{1}=\frac{y-0}{0}=\frac{z-0}{0}\tag1$$ according to the formula ...
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1answer
15 views

Angular momentum superposition

I am doing a space simulation. I have a spaceship and this spaceship has engines that don't push the spaceship through its center of gravity. These engines can therefore give the spaceship angular ...
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1answer
25 views

doubt with direction angles

Is it possible for a 3D vector to be drawn with the direction angles of $\alpha=45^\circ$ and $\beta=45^\circ$ ? if yes what is measure of $\gamma^\circ$? I calculated $\cos^2(45^\circ ...
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1answer
14 views

Get direction of normal without matrix inversion

I am building a 3D engine and I want it to calculate normals for triangles automatically. The user creates a model that is made of triangles. Every triangle is made of three points in the space, and ...
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1answer
21 views

Reflecting a line from plane

I have a plane given by equation $0=10x+2y-3z$ and a line described by vector with variable $t\ge0$ $(1-t, 1+2t, 1+t)$ How to calculate reflected vector of this line from plane? We treat line as ...
2
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2answers
45 views

What makes the inside of a shape the inside?

A question occurred to me when browsing SE this evening, just curious. What specifies the inside of a 3D construct? If I have a hollow sphere, what's to say that the world isn't the inside, and the ...
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0answers
8 views

Question about the projection of a 3-d region onto the $xz$-plane

How do they get that $D_3$, below? Express the iterated integral as a triple integral: $\int_0^1 \int_0^{x^2} \int_0^y f(x,y,z)\ dz\ dy\ dx$. The projection of the region on the: $xy$-plane: ...
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2answers
17 views

Coplanarity of two lines in 3D

Suppose we have 2 lines $$l_1 : x = 5 , \frac{y}{3-\alpha}=\frac{z}{-2}$$ and $$ l_2: x= \alpha , \frac{y}{-1}= \frac{z}{2-\alpha}$$ so what will be value of $\alpha$ for lines to be coplaner ? I ...
2
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1answer
279 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 ...
0
votes
0answers
24 views

2d to 3d projection problem

I am writing a software where user can add objects in the 3d space and I want to make the user to be able to drag those objects with the mouse. Whenever my mouse moves I have an event fired ...
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2answers
38 views

Estimating the missing points of a 3D point cloud

Consider a cloud of N points (forming a smooth 3D object), in which n points are missing. Also, consider that there is no prior knowledge about the original shape of the point cloud. The only ...
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0answers
17 views

Best fitting circle to points in 3D

I have a set of n ≥ 3 points in 3D that are measurements of a possible circle. The measured points are "noisy" so best-fitting algorithms are involved. I'm programming in C# and have put together some ...
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1answer
36 views

Using several curves in 3D to create a surface

I have a set of several closed curves in 3d (like image below is showing my set of curves from 3 views). To clarify my idea, i ask my questions in two different ways showed by diction 1 and diction ...
3
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2answers
44 views

Reflections on a sphere

There is a sphere located in a point s with radius r. The Sphere is a perfect mirror. If i'm sitting in the point c, I want to cast a ray to the sphere such that I hit the point p after bouncing in ...
0
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1answer
26 views

Shortest distance between two given lines (Hint)

There seems to be this question that I can't seem to be able to solve. I'm hoping someone could help me figure out how to solve it. Question: Find the shortest distance between the lines ...
2
votes
2answers
34 views

Midpoint of the shortest distance between 2 rays in 3D

I would like to come with an algorithm to find the midpoint of the shortest between 2 rays a+tb and c+sd, where t and s are scalars. I have a scenario which I try to depict like this. One of the ...
3
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3answers
142 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
40 views

How to draw or plot illustrative figures?

stackexchange users I would like to plot or draw some illustrative figures for my research paper. I've tried GeoGebra already. But couldn't draw them as I wanted. So my question is How can I draw ...
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0answers
25 views

Triple integral, finding the volume between two planes and a surface in 3D

So I have tried to solve this problem, but I'm running into a problem, because the top circle (intersection of the function with z=1) when you project it onto the xy plane is smaller than the circle ...
0
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0answers
15 views

How to do the calculation of the error in positioning in 3D Space?

I'm mathematically calculating a position on given data in a program. But I need to validate that the calculated values against the original position value. If the Original position is Xi,Yi and Zi ...
0
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0answers
13 views

parametric representations 3d object

I'm trying to model a 3 dimensional body that is sort of ellipsoidal and am looking for parametric representation of 3D objects similar to the quadratic surface representation of a sphere or ...