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
44 views

Help me find the function behind this data?

I have a function $f(x, y)$ and I have another (non-mathematical) algorithm capable of inefficiently generating the exact same results as in in a 'brute force' manner. Since I have been able to find ...
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1answer
77 views

Rotating an object correctly when you can only rotate world axis.

This question may be useful to some people, but it is not posed correctly for my particular situation, please see: Simulating simultaneous rotation of an object about a fixed origin given limited ...
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2answers
42 views

How to determine the distance to one point from another in a 3D coordinate system?

I wonder how I can calculate the distance between two coordinates in a $3D$ coordinate-system. Like this. I've read about the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ (How) Can ...
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2answers
109 views

Why is the volume one third of that? I mean, where's the fault in my logic? [duplicate]

The volume of a cuboid is $l \times b \times h$. That is, it is equal to base area times height. I think it means that the base is added up height times, it becomes volume (It makes sense if we think ...
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3answers
285 views

Is there a generalization of the Lagrange polynomial to 3D?

What is a way to construct a smooth polynomial surface ($\mathbb{R}^2 \rightarrow \mathbb{R}$) with Lagrange-polynomial properties in every partial derivative? I want to try this for image ...
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1answer
74 views

Arc length of a 3D Curve

I have a set of points in 3D space: $$\left(x_i, y_i, z_i\right)$$ These points create a 3D curve and I am trying to calculate its arc length. I have followed what is described here but when I ...
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1answer
76 views

Looking for help for building a Spline's algorithm 10th order

I'm trying to code the following algorithm in C++ and need help to understand the build of Splines from a mathematical point of view (found on page 129 on this paper). $$ f(t) = \boldsymbol{t} \cdot ...
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1answer
18 views

Velocity vector transformations with respect to a global frame of reference

This seems like it should be a simple problem, but I've been stuck on it for about a day now. It's technically a programming problem, but I'm posting it here because the root of the problem is really ...
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2answers
138 views

How can I convert camera motion into zoom?

I try to reconstruct a camera of a video sequence via match moving techniques. After the reconstruction process all seemed to work as expected, but then I've realized my camera is moving forward ...
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3answers
203 views

Point inside a tetrahedron joined to corners creates how many new internal planes?

When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? How do we ...
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0answers
24 views

Sections of cones in higher dimensions

Everybody knows that when a plane intersects a cone at different angles and positions, we get conic sections. But, I wanted to know that if the same was possible in higher dimensions. If we take the 4 ...
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1answer
17 views

Descretizing an arbitrary plane in 3D

I have a plane in 3D with size $L1\times L2$ with arbitrary orientation. The normal to the plane is $\vec{n}$. I am trying to descretize this plane into $N1\times N2$ grids. I want to have the ...
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1answer
35 views

Curve on a torus

Consider a curve $f$ that connects two arbitrary points on a torus. What are the equations that defines the curve $f_{min}$ whose such a distance is minimal?
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1answer
30 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
48 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
54 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
57 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
49 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
94 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
48 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
188 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
72 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
88 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
74 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
43 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
66 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
37 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
104 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
42 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
34 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
44 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
21 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
314 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
21 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
25 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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0answers
11 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
51 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
30 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
33 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
126 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
119 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
58 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
37 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 ...