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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1answer
37 views

Can a 1-side, 1-border object exist in 3D?

We are three friends discussing whether a three dimensional object with a single side and a single are can possibly exist. I first came up with a Moebius strip as an affirmative example The second ...
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3answers
49 views

Finding Tangent Line to Graph

Find a vector equation for the tangent line to the curve of intersection of the cylinders $\ x^2 + y^2 = 25$ and $\ y^2 + z^2 = 25$ at the point (3,4,2). I don't understand the answer key. I've ...
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2answers
50 views

Stuck on a 3d equation

I have three 3D points with an known Z value: point 1 = (0, 0, Z1) point 2 = (64, 0, Z2) point 3 = (64, 64, Z3) I need an equation to solve for the Z value given ...
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1answer
66 views

Understanding normal and binormal of a vector or of a spline

I found a paper where it computes the 3D trajectory of a quadrotor and defines an error position as the difference between 2 vectors (here the source, under 3D trajectory control): $$ e_{p} = ...
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1answer
58 views

Linear equations in 3D space [duplicate]

I need to search a line in a 3D space. I have a starting point (coordinates) of the line and the angle at which it is suppose to go (relative to each of the axis). I need to start from the starting ...
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1answer
59 views

Hyperbolic paraboloid: how to find the distance from a point on the surface to the $z$-axis?

The given hyperbolic paraboloid is $z=xy$. How do I find the distance $r$ from a point on the surface to the $z$-axis? I used a function grapher to visualize the 3-D surface. But I am unable to ...
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2answers
108 views

Determining the equation of this 3D object

Does anyone know how I can determine the equation of the 3D object below? (Maybe there's a program that can do it?) I am looking for a formula to define this 3D object, but am having trouble finding ...
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0answers
51 views

How can we split a single rotation into two along orthogonal axes?

I have the following axis system, where the X-Y plane is horizontal and Z points 'up': I have a horizontal plane that I want to rotate so that the angle between it and the XY plane is theta. I ...
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3answers
266 views

3D coordinates of circle center given three point on the circle.

Given the three coordinates $(x_1, y_1, z_1)$, $(x_2, y_2, z_2)$, $(x_3, y_3, z_3)$ defining a circle in 3D space, how to find the coordinates of the center of the circle $(x_0, y_0, z_0)$?
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1answer
30 views

Construct a procedure which determines the location of the shadow of a rectangluar box.

I drew a 3d rectangular box on a coordinate plan consisting of x, y, and z. A procedure is to be created that will determine the location of the shadow of the box on one of the coordinate planes. I ...
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0answers
26 views

Non-standard 3D rotation of a set of points [duplicate]

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
97 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 ...
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1answer
99 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 ...
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1answer
98 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
51 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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1answer
113 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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0answers
44 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
133 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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0answers
44 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
12 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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1answer
39 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
16 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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1answer
46 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
23 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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5answers
317 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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1answer
22 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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0answers
14 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
54 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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1answer
29 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 ...
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1answer
32 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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2answers
36 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 ...
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1answer
152 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
126 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 ...
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2answers
63 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 ...
12
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1answer
217 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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1answer
43 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 ...
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4answers
191 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 ...
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2answers
89 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 ...
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2answers
30 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
77 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
134 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 ...
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0answers
24 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 ...
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0answers
77 views

From Icosahedron to Pentagonal hexecontahedron (Floret Tessellation)

Inspired by this post: Floret Tessellation of a Sphere I tried to transform myself an icosahedron into its simplest Floret tessellation. But I am having trouble when applying the 'method' given in the ...
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0answers
36 views

Unique representation of each point in 3d space by Linear combination of 3 mutually perpendicular vectors.

I intuitively accepted that there is an unique representation of any point in a 3d space by linear combination of 3 mutually perp. vectors. But now I'm wondering is this an axiom or a theorem? If ...
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1answer
44 views

Flatten 3D VectorA so it's perpendicular to VectorB

Basically I have 2 3D vectors: Vector A (green) and vector B(red). I need to calculate a third vector that is perpendicular to VectorA (green) but points in the same direction than VectorB (red). ...
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0answers
37 views

Inertia tensor of a triangle in 3d

I am computing inertia tensor of a triangle given by its 3 vertices. The tensor should be computed at some local origin. I used covariance as explained in this Wikipedia article, but I am not sure ...
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0answers
159 views

3D equation of a cone-like shape

Imagine there are two parallel planes (base plane and plane1) in the following image: There is one point on the base plane and there are several points on the plane1. The positions of these points ...
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1answer
114 views

Is it true that a arbitrary 3D rotation can be composed with two rotations constrained to have their axes in the same plane?

I am interested in decomposing an arbitrary rotation in 3D space into the product of two rotations which are constrained to have their axes in the same plane (for instance x-y plane). Statement of ...
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0answers
33 views

What the Surface function will it be if a circle tilted with an angle and then rotating around z axis

My first idea is this will result in a elliptic torus. The horizontal semi-axis a=R and the vertical semi-axis b=R*cos(beta). assuming the titled or inclined angle is beta. The distance away from ...
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0answers
33 views

unique cube arrangments

i have received this math riddle which i cannot solve, the riddle: given a set of cubes, a unique shape is any shape that was created joining cubes sides together and does not match any previously ...