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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Quaternion Rotation

I am modelling rotations of a rectangular box (3 dimensions) in Matlab using Quaternion theory. Using the theory found on https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation I have ...
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0answers
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In 3dimension, How to move the vector to the point? [on hold]

In 3D, I want to move my point to target point side. And my point has direction. By the way, I must move in direction of my point. If direction of my point same position of target, I have to move my ...
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1answer
17 views

What is the equation for the number of combinations of 4 cubes that can be rotated on all axes

I have been trying to work out the number of possible unique combinations of 4 cubes where they can be rotated on any axis. So for example if all the faces of all the cubes where unique across the ...
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1answer
19 views

Inverse Parameters of a Pan-Tilt Rotation Possible?

I have a 2-parameter (tilt,pan) rotation computed as tilt followed by pan, i.e. two rotation matrices multiplied together: $$R(t,p)=\begin{pmatrix} c_p & s_p s_t & s_p c_t \\ 0 & c_t &...
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1answer
18 views

Computing new 3D coordinates given time and linear velocity

Assume that an object in a 3D space has a position $\displaystyle {x}, {y}, {z}$ and a linear velocity $\displaystyle v_{x}, v_{y}, v_{z}$ Can I predict the new $\displaystyle {x}, {y}, {z}$ position ...
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2answers
91 views
+100

How do I calculate this loop spline given the length, angle and horizontal offset?

I'm developing a formula to calculate a loop spline from a length, angle and horizontal offset. I can successfully calculate the loop from the first two parameters, but taking the horizontal offset ...
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0answers
19 views

Calculating fov angle based on distance

I'm trying to calculate the angle between me and the target angle yaw in a 3D game, so that the actual angle is always the same based on distance how far I am from the target. I've tried a few ...
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1answer
36 views

Find all near points in a large array of points

Simplified problem: I have an array of points in 3D space. I want to find all pairs that are within a given distance from each other. (I'm writing a very simple simulation and the points merge into a ...
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2answers
28 views

Normal to surface at point

I have this function: $F(x,y,z)=x^2−y^2−z^2+4$ where $z\ge 0,0\le x \le 2,0 \le y \le 2$. How can I find the normal at some point $P=(p_x,p_y,p_z)$? I have tried to calculate the derivatives of ...
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0answers
14 views

Scaling in world space

In a hierarchical transformation system, where a node has one parent and children (Tree form) I want to scale an object with respect to world space axis. My transformation order is (Translate * Rotate ...
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0answers
16 views

Finding all three components (x, y, z) of a 3d vector using direction angles and the vector magnitude

I have the alpha, beta, and gamma direction angles of a certain vector. I also have the magnitude of this vector. These angles are being determined by a gyroscope mounted on a Quad-copter. Since ...
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0answers
15 views

Absolute value of an RBF distance is less than the absolute value of an actual distance

I have a radial basis function with a linear kernel f(r)=r in 3D. I constructed the surface based on this RBF and noticed that the absolute value of actual distance from any point to the constructed ...
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1answer
45 views

Finding the parameters of an ellipsoid given its quadratic form

Suppose we have the quadratic form of an ellipsoid of the form $$ax^2 + by^2+cz^2+dxy+eyz+fxz+gx+hy+iz+j=0$$ I want to find centroid of the arbitrarily oriented ellipsoid, its semi-axes, and the ...
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0answers
38 views

Equations of the tangent planes to the sphere

Find the equations of the tangent planes to the sphere $x^2+y^2+z^2-10x+2y+26z-113=0$ which are parallel to the straight lines $\frac{x+5}{2}=\frac{y-1}{-3}=\frac{z+13}{2}$ and $\frac{x+7}{3}=\frac{y+...
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0answers
20 views

Newtonian potential of homogeneous ball

Let $x \in B_R(0) \subset \mathbb{R^3}$. To compute $$u(x)=\int_{B_R(0)} \frac{1}{|y-x|} dy$$ The integrand has singularity at $x$, so consider $$u_\epsilon(x)=\int_{\substack{|y|< R \\ |y- x|> ...
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0answers
39 views

Proof that there exists a 3d representation of all graphs

Below is a question and proof that I've done. I was wondering if there is a more formal way of concluding a point must exist that is not in a set composed of a finite number planes. Currently I am ...
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4answers
62 views

The formula for 3D rotation of the perspective of an image in 2D space

Do you know what the formula is for the 3D rotation of the perspective of a 3D object in a 2D space. For example, imagine that we got a picture of a 3D object. So, we have the projected picture of ...
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2answers
22 views

Formula For 3D Dilation?

If I have a sphere on a 3D grid with it's center being at the origin, and I want to double the size of the sphere, where would it's poles be?
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1answer
28 views

Efficient assignment of tetrahedron's chirality

Suppose we have a regular tetrahedron delimited by four points $A_{1}, A_{2}, A_{3}, A_{4}$. There are 24 permutations of vertices, but there are only two distinct terahedra that cannot be ...
2
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1answer
19 views

Non-trivial 3D curve that projects as a line or a segment onto the faces of the quadrant

I want to illustrate how high dimensional objects may have misleading projections. Examples are for instance given with HiSee software, with nD bouquets of circles. Are there non-trivial (not a 3D ...
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0answers
26 views

Translation by tensors

According to this question, quaternions would not be the right choice to handle both rotation and translation. In the case of tensors, one might assert that the rotation would be possible by tensors, ...
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1answer
15 views

3-Space Vertices of a Parallelogram

The points (1, -2, 4), (3, 5, 7) and (4, 6, 8) are three of four vertices of parallelogram ABCD. Explain why there are three possibilities for the location of the fourth vertex, and find the three ...
2
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1answer
28 views

Determining angle of view from an image with a square or checkerboard in the background.

I take a picture of a square of known dimension (let's say 1x1 units) with the camera at an unknown angle relative to the plane of the rectangle. (The distance to the rectangle is also unknown, but ...
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1answer
49 views

Can there be a limit cycle without a fixed point in 3D space?

I am working with a population dynamics model. Basically, I have a nonlinear ODE in $R^3$ space, (X,Y,Z), and I know that if I start in the an open region ($0<X<1,0<Y<1,0<Z<1$, ...
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0answers
29 views

Counting balls in face centred cubic close packing

Possibly too easy for stack exchange, but... Consider a cubic close packing, or face centred cubic, arrangement of balls or radius $1$ in dimension $3$. Suppose that the origin is the centre of one ...
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0answers
35 views

Euler Angle + Distance to XYZ coordinate

Background I'm familiar with Euler Angles and 3d space systems but I'm having trouble with Rotation Matrices. Scenario I've converted my Euler Angle to degrees for ...
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0answers
44 views

Given set of points in 3D, find group of points closest to each other

Given a set of any 8 points in 3D space. I want to find a subset of points that are closest to each other. Application: Assume in a 3D space, I have any 8 colors(represented in RGB). I know how to ...
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0answers
48 views

Draw a line between an observer and the current direction of the sun

My goal is to draw a line between an observer and the current direction of the sun. Given the observers coordinates (Lat, Lon) of (51.50442, -0.08630) a North of (90, 0), an Azimuth of 270 degrees ...
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0answers
27 views

How to determine the equation of shortest path on any 3d surface between two given points?

I am working on draping of woven composite and I have to determine the equation of shortest path on 3D surface (i.e. $z=x^2+y^2$) between two given points in order to get the yarn path between two ...
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1answer
46 views

Can two lines lying in different plane be parallel?

In two lines lie in different plane, can they be parallel to each other? I am thinking if two lines are parallel to each other, then their direction cosines must be same so two lines lying in ...
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0answers
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Find radius of curvature of a $3D$ surface at a point if the tangent vector at that point is given.

I have a $3D$ surface with equation $z=x^2 +y^2$ and need to find the radius of curvature at a point $P(x_1,y_1,z_1)$ using the tangent vector at that point. Since, there are many possible radii of ...
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2answers
33 views

Plotting a 3D graph from explicit equation

I´m a 2nd year engineering student and today we learned how to plot 3d graphs from a $XYZ$ equation on paper. For example, I know ($\frac{X^2}{9}+ \frac{Y^2}{16} + \frac{Z^2}{9} =1$) will produce an ...
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1answer
74 views

A 3d integral over a ball

Given $a \in \mathbb{R}^3$ and $r>0$, is it possible to compute $$\int_{B_r(a)} \frac{a\cdot x}{|x|^3} dx$$ where $B_r(a)$ is the ball in $\mathbb{R}^3$ with radius $r$ and centered at $a$.
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2answers
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Quaternion interpolation in 3D

I'm a chemist lost in the captivating world of mathematics thus if you could keep your answers simple it would be awesome! Here is my problem: I have two mobiles (A,B) in 3D. Ideally, I would like to ...
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1answer
29 views

How to compute the pivot point of a rectangular cuboid to achieve a certain rotation?

Summary: For a video game project, I have an object (craft) that hovers the ground using a soft constraint. Imagine that on the picture below there is an invisible point above the craft whose ...
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3answers
60 views

Find the equation of the sphere which touches the sphere $x^2+y^2+z^2+2x-6y+1=0$ at $(1,2,-2)$ and pass through $(1,-1,0)$

Find the equation of the sphere which touches the sphere $x^2+y^2+z^2+2x-6y+1=0$ at $(1,2,-2)$ and pass through $(1,-1,0)$ My Attempt: Let the equation of the sphere be $x^2+y^2+z^2+2ux+2vy+2wz+d=0$...
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1answer
21 views

Find the equations of the tangent planes to the sphere $x^2+y^2+z^2+2x-4y+6z-7=0,$ which intersect in the line $6x-3y-23=0=3z+2.$

Find the equations of the tangent planes to the sphere $x^2+y^2+z^2+2x-4y+6z-7=0,$ which intersect in the line $6x-3y-23=0=3z+2.$ Let the tangent planes be $A_1x+B_1y+C_1z+D_1=0$ and $A_2x+B_2y+...
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1answer
35 views

Prove that as $PP'$ varies,the circle generates the surface $(x^2+y^2+z^2)(\frac{x^2}{a^2}+\frac{y^2}{b^2})=x^2+y^2.$

$POP'$ is a variable diameter of the ellipse $z=0,\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$ and a circle is described in the plane $PP'ZZ'$ on $PP'$ as diameter.Prove that as $PP'$ varies,the circle ...
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1answer
74 views

Locus of the center of the circle of radius $a$,which always intersects coordinate axes

If the axes are rectangular, show that the locus of the center of the circle of radius $a$,which always intersects coordinate axes is $x\sqrt{a^2-y^2-z^2}+y\sqrt{a^2-z^2-x^2}+z\sqrt{a^2-x^2-y^2}=a^2$ ...
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4answers
65 views

Find the center of the circle through the points $(-1,0,0),(0,2,0),(0,0,3).$

Find the center of the circle through the points $(-1,0,0),(0,2,0),(0,0,3).$ Let the circle passes through the sphere $x^2+y^2+z^2+2ux+2vy+2wz+d=0$ and the plane $Ax+By+Cz+D=0$ So the equation of ...
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1answer
68 views

3D Perspective projection

I have this following question to answer, however I am not sure how I should combine my calculation into one final answer. Suppose the Centre of Projection in a viewing space is at an offset $(0,...
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1answer
138 views

Photo image to find the screen orientation

I am trying to find the angle of tilts of a screen using projection of a circle from a source $S$. The light beam falls on the photo screen to expose it and what we get is an ellipse with major axis $...
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1answer
11 views

Find the equation of the sphere $OABC.$

$OA,OB,OC$ are mutually perpendicular lines through the origin and their direction cosines are $l_1,m_1,n_1;l_2,m_2,n_2;l_3,m_3,n_3.$If $OA=a,OB=b,OC=c,$prove that the equation of the sphere $OABC$ is ...
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0answers
14 views

Show that the center of the sphere lies on the line $z=0,x^2+y^2=(a^2-c^2)\csc^22\alpha$

A variable sphere passes through the points $(0,0,\pm c)$ and cuts the lines $y=x\tan\alpha$, $z=c$; $y=-x\tan\alpha$, $z=-c$ in the points $P,P'$. If $PP'$ has constant length $2a$ show that the ...
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3answers
50 views

Obtain the equation of the sphere which passes through the points $(1,0,0),(0,1,0),(0,0,1)$ and has its radius as small as possible.

Obtain the equation of the sphere which passes through the points $(1,0,0),(0,1,0),(0,0,1)$ and has its radius as small as possible. Let the sphere passes through $(x_1,y_1,z_1)$ Then i obtained ...
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1answer
23 views

Find 2D plane in the center of nonlinear 3D object

I'm building a segmentation algorithm. I'm segmenting pieces of paper in a book that have been slightly crumpled. Imagine taking a piece of paper, crumpling it into a ball, and then trying to ...
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2answers
42 views

Fitting point to plane??

As explained here, given a plane: ax + by + cz + d = 0 and a point x0=( x0 , y0, z0 ), the normal vector to the plane is given by: v = [ a ; b ; c ] and a vector from the plane to the ...
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0answers
21 views

Cylinder ray puzzle

A set of rays (imaginary beams, no direct relation to other concepts) are shot from various points in a cylinder forward and and backwards until they reach the edge of the cylinder. The rays' forward ...
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0answers
24 views

warping a cube in a 3d space

3D cube made with Octave The problem I have is shown in the picture above. I have 2 cubes where both cubes are filled with vectors, or have possible vector locations. The blue cube is filled normally,...
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0answers
24 views

How to calculate pixel location of object in 3D world

I have developed a 3d game and I have a box object off in the distance on a hill and I want to calculate the on screen pixel location for each of the four corners of the box so I can put an overlay on ...