# Tagged Questions

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.

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 ...
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.
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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 ...
5k views

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 $x^2+y^2+z^2+2ux+2vy+2wz+d=0$...
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 ...
20 views

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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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,...
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 ...
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 ...