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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2
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1answer
559 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 ...
2
votes
2answers
774 views

What is an isosurface?

I am trying to understand the marching cubes algorithm. I would like very much an easier definition of an isosurface than what is available online. Could anyone please explain it? Thanks.
1
vote
3answers
881 views

Identify and sketch the quadric surface?

I'm stuck trying to figure out which type of quadric surface this equation is: $$\dfrac{x^2}{16} - \dfrac{y^2}{9} - \dfrac{z^2}{1} = 1$$ I have narrowed it down to a hyperboloid, but cannot ...
1
vote
1answer
25 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
votes
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 ...
-1
votes
0answers
28 views

Area of cross section in the intersection of two cylinders

A Steinmetz solid "B" is formed on the intersection of two cylinders, given as: x^2 + z^2 = r^2 and y^2 + z^2 = r^2 Although, referring to Gardner's work, I have successfully calculated the total ...
-1
votes
0answers
11 views

Best 3D reconstruction method.

I'm looking for a method to generate a 3D point cloud from one or more cameras (I know the position of each camera). I need the point cloud to be generated each frame (of video from the camera) and ...
2
votes
2answers
8k views

How to find line parallel to direction vector and passing through a specific point?

I am give the point $(1,0,-3)$ and the vector $2i-4j+5k$ Find the equation of the line parallel to vector and passing through point $(1,0,-3)$ Could one use the fact that the dot product between the ...
1
vote
0answers
25 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, ...
1
vote
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 ...
0
votes
1answer
636 views

Calculating normals for a polygon mesh (3D computer graphics)

I want to write a program to generate arches, a common architectural form, and export them to a wavefront object format for sharing with various three dimensional graphics editors. To do this, I need ...
2
votes
1answer
26 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 ...
3
votes
1answer
5k views

How to find perpendicular distance from point to plane in $3D$.

The line $L_1$ passes through point $A$ whose position vector is $3i - 5j + 4k$, and is parallel to the vector $3i + 4j + 2k$. The line $L_2$ passes through the point $B$ whose position vector is $2i +...
-1
votes
0answers
7 views

3d-Geometry (paraboloid). Finding the tangent plane

Tangent Planes at two points P and Q of a parabolid mmet in a line RS. show that tthe plane through RS and middle point of PQ is parallel to axis of parabola.
3
votes
1answer
1k views

Jacobian of exponential mapping in SO3/SE3

Following this post Jacobian matrix of the Rodrigues' formula (exponential map) What if I really need the Jacobian of the exponential mapping function in $\omega \neq 0$? Basically, I want to ...
1
vote
2answers
117 views

**Location** of shortest distance between two skew lines in 3D?

I can find the shortest distance $d$ between two skew lines $\vec{V_1}$ and $\vec{V_2}$ in 3D space with $d=\left|\frac{(\vec{V_1}\times\vec{V_2})\cdot\vec{P_1P_2}}{|\vec{V_1}\times\vec{V_2}|}\right|$...
0
votes
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 ...
0
votes
1answer
68 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 $x\sqrt{a^2-y^2-z^2}+y\sqrt{a^2-z^2-x^2}+z\sqrt{a^2-x^2-y^2}=a^2$ ...
1
vote
1answer
47 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 ($0<X<1,0<Y<1,0<Z<1$, ...
0
votes
1answer
75 views

Trigonometric Word Problem in 3D

The question I am having trouble on is as follows: "As an Expert Mathematics Witness, you have been presented with a Ballistics Report, and a Police Report as your evidence. Use the information ...
0
votes
0answers
27 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 ...
3
votes
2answers
401 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 ...
0
votes
0answers
35 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 ...
0
votes
0answers
46 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 ...
0
votes
0answers
34 views

How can I flatten/ represent or map the points on 3D surface in 2D plane? [closed]

I am having some points on sphere and I want to represent these points on 2D surface. It would be better or easy to understand if you can explain with some example.
1
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0answers
25 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 ...
1
vote
1answer
33 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 ...
2
votes
1answer
94 views

What should happen to an impossible cube at a vertex?

I have automated the process of impossible-cube renders in Blender3D as an exercise. However, while the automator works fine as long as the intersection of the 'impossible' edge and the nearer edge is ...
3
votes
2answers
41 views

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 ...
0
votes
1answer
40 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 ...
0
votes
0answers
20 views

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 ...
0
votes
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 ...
0
votes
1answer
69 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 $a$.
0
votes
1answer
27 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 ...
1
vote
1answer
478 views

How to find the points of intersection of the perpendicular vector two skew lines

Correct me if im wrong, but this is what i know so far The cross product of two skew lines is the perpendicular vector between both those lines. The perpendicular vector intersecting two skew lines ...
7
votes
1answer
137 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 $...
1
vote
3answers
53 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 $x^2+y^2+z^2+2ux+2vy+2wz+d=0$...
1
vote
3answers
2k views

Minimum distance between point and face

Given a point in 3D space of the form (x, y, z) and a triangle consisting of 3 vectors (also in the (x, y, z) format), how would I calculate the minimum distance between the point and the face of the ...
1
vote
1answer
20 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+...
1
vote
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 ...
3
votes
1answer
64 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,...
0
votes
1answer
10 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 ...
0
votes
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 ...
1
vote
3answers
43 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 ...
0
votes
2answers
40 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 ...
0
votes
2answers
120 views

x(u,v), y(u,v), z(u,v) parametric equations for a special cycloid

I'm trying to find out 3D parametric equations for a cycloid. I know that a cycloid is a 2D curve that is generated by a point on a rolling circle. But my circle is rolling around another circle, and ...
1
vote
1answer
22 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 ...
0
votes
0answers
22 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,...
0
votes
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 ...
0
votes
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 ...