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.

learn more… | top users | synonyms

0
votes
1answer
30 views

Reflection of a plane on a plane

How to find the reflection of the plane $ax+by+cz+d=0$ in the plane $a'x+b'y+c'z+d'=0$? I can't really think of a method of for doing so. I do know how to reflect a line on a plane though.That ...
0
votes
0answers
44 views

Why is cot(a) function used in perspective projection?

I'm working with the different space projections. But I wonder about the perspective projection. Let me remind you one template, which may be used in 3D rendering software: ...
1
vote
4answers
144 views

How do I find the image of a point in a line in 3D space?

The question is, find the image of the point $(1, 6, 3)$ in the line $$\frac x1 = \frac {y-1}{2} = \frac {z-2}{3}$$ I want to know the general equation to find the image of a point in a line. ...
4
votes
2answers
58 views

Locus formed by point on a line intersecting 3 other lines in 3D

I got this particular question from an old test paper... Consider three lines given by $y-2=z+3=0$; $z-3=x+1=0$; $x-1=y+2=0$. Let $(\alpha,\beta,\gamma)$ be a point lying on a line intersecting ...
-1
votes
1answer
42 views

Finding angle between straight lines whose direction cosines are implicitly given

Prove that the angle between the straight lines whose direction cosines are $l,m,n$ are given by $l+m+n=0$ and $fmn+gnl+hlm=0$ is $\pi\over 3$ if $1\over f$ +$1\over g$+$1\over h$=$0$. Also ...
0
votes
1answer
33 views

Projection of a plane on coordinate planes

$$\left|\begin{matrix} x & y & z & 1 \\ x_1 & y_1 & z_1 & 1 \\ x_2 & y_2 & z_2 & 1 \\ x_3 & y_3 & z_3 & 1 \end{matrix}\right|=0$$ This is the equation ...
4
votes
3answers
128 views

Which particular pair of straight lines does this equation represent on putting $z=0$?

Suppose we have a joint equation of planes $8x^2-3y^2-10z^2+10xy+17yz+2xz=0$.Suppose we put $z=0$ we get a joint equation of pair of straight lines. Now which particular pair of straight lines does ...
0
votes
0answers
19 views

Linear interpolation from perspective-correct interpolators

This question is trying to approach this problem from a mathematical perspective. I have some value $u$ that I want to interpolate linearly, as $(1-a)u_0+a u_1$. However, I can only use ...
0
votes
0answers
30 views

Calculate the size of the shadow from a cube onto another cube

There is a big cube with a light (point) exactly in the middle of it. Then there's also a small cube inside that big cube. My task is to calculate the surface of the shadow (sharp edges, no shadow ...
0
votes
1answer
17 views

2d rotation matrix derivation

I was reading this article here and i understand the equation until the part when he replace the r with x or y ,, so i know that cos = adj/hyp and sin = opp / hyp ,,, and to calc both values we need ...
0
votes
2answers
51 views

Using dot product when finding shortest distance between a line and a point, not working

Question goes as follows: Consider the points on a line; $A(1,3,-1)$ and $B(-1,4,-2)$. Find the point $Q$ on $L$ closest to the point $P(1,1,0)$. My thinking: Closest distance from $a$ to $b$ is ...
0
votes
0answers
42 views

rotate geometry along curve velocity without roll

I am a programmer and I'm writing a script that turns any 3D function into a 3d tube (discrete geometry). In this example I have a bezier curve f that loops and a set of vertex offsets V that ...
0
votes
1answer
26 views

Volume between $z = 3\sqrt{x^{2} + y^{2}}$ and $x^{2} + (y-1)^{2} = 1$ and $z = 0$

Find the volume between $z = 3\sqrt{x^{2} + y^{2}}$ and $x^{2} + (y-1)^{2} = 1$ and $z = 0$ I am not sure how to approach finding the limits of integration. Would I need to change coordinate ...
0
votes
2answers
37 views

How can I derive equation of line in 3d?

I started studying 3d geometry and wanted to know how to derive equation of line in 3d from vectors.the equation is r=a+kb.
1
vote
2answers
73 views

The volumes of two similar cylinders.

The two cylinders have the same heights and the radius of the cylinder B is two times the radius of cylinder A. The volume of A is $1$ and we're interested in the volume of cylinder B. Since The ...
0
votes
0answers
43 views

Metric Image Rectification using Camera Angle and Focal Length

I'm trying to measure the size of an object in millimetres from an close-range image of the object captured with an angled camera. The application is intended to be from a smartphone, so we can't ...
0
votes
1answer
20 views

Midpoint of two line segments in three dimensions

This might be an easy question, but since i'm new to solid shapes, i couldn't solve it. A= (7,1,3) B=(5,1,2) C=(4,-2,3) D=(6,m,n) I need to find m and n so that segments BD and AC have the smae ...
0
votes
1answer
111 views

Finding the radius of a circle when a sphere is cut by a plane.

This is the question: Let $S$ be the sphere of radius $14$ centered at the point $C(5, −3, 16)$. (a) The plane $y = 3$ intersects $S$ in a circle. Where is the centre of this circle and what is its ...
0
votes
0answers
11 views

Identifying a 3D Figure fromed from a hexagonal cross section

I have the curves: $$f(x)=\dfrac{|(x-2)(x+6)|}{2}$$ $$g(x)=-\dfrac{(x+3)^2}{2}+9$$ on the domain $\left(-7,\frac{1}{2}\right)$ and have hexagonal cross sections with the two vertices on an edge on the ...
1
vote
0answers
28 views

Circle homography

I'm attending a 3d-graphics course and I want to figure out which homograpic transformations conserve a circle's equation. The circle's equation is given as: Circle = $x^2 + y^2 + Ax + By + C = 0 $ ...
0
votes
0answers
29 views

Construct 3D plane from 2 points and minimize angle of two vectors with its normal

I have as input two points $P, Q \in E^3$ and two vectors $\vec{v}_1, \vec{v}_2 \in R^3$. I need to construct a plane $(\vec{n}, d)$ such that the two points are in the plane and the angles between ...
1
vote
1answer
30 views

Show right angles for orthogonal vectors in 3D

This question is one of simple computational geometry, similar to what I posted in http://stackoverflow.com/questions/34186711/rgl-vector-diagrams-show-right-angles-for-orthogonal-vectors. But no one ...
0
votes
0answers
27 views

3D graphics: Sphere intersection occlusion

Suppose I have two solid spheres $s_1$ and $s_2$ (and by solid spheres I mean 'balls' in the strict mathematical sense). We know their centres and radii, and we know that they have some overlapping ...
1
vote
1answer
20 views

Given a start point in 3d and a quaternion and length to Point B can you find Point B

Let's assume I have a start point A (x, y, z). Now the object has moved and the new orientation is given by a quaternion Q and it's pointing at point B which is L length away from it. How can I ...
0
votes
1answer
154 views

Find points of Rectangle given two diagonal points and a normal in 3D

I'm developing a geometry framework in a program I'm working on that contains all the good stuff like vectors, points, lines, planes, polygons, etc. I was attempting to create a rectangle object, but ...
0
votes
1answer
25 views

What would be a description of this set in $\mathbb R^3$?

Suppose that $K=\{(x,y,z)\in \mathbb R^3|x\geq 0,y\geq 0, xy\geq z^2\}$. Let $K_0=\{x\in\mathbb R^3|\langle x,k\rangle\leq 0\forall k\in K\}$. What would be a description of the set $K_0$? I don't ...
0
votes
0answers
18 views

Finding equation of a plane normal to an intersection curve

The cone with equation $z^2=x^2+y^2$ and the plane with equation $2x+3y+4z=-2$ intersect in an ellipse. Find the equation of the plane normal to the ellipse at the point $P(3,4,-5)$. I try to find ...
0
votes
2answers
42 views

3D shape with orthogonal projections that form circles of the same radius.

Let's say you have a 3D shape. The side view, front view, and top view of the shape are all circles of the same radius. Does the shape have to be a sphere, or is it possible that it could be another ...
0
votes
0answers
16 views

Finding vector components and converting terminal point to cylindrical coordinates

Is my logic correct in finding the component form of vector v? The questions are below. For part a, since the vector is in the yz-plane, I wrote the vector as a 2D vector showing only the y and z ...
1
vote
1answer
29 views

$e^{-\frac{1}{x}}e^{-\frac{1}{1-x}}$ in 3D

I have the function $f(x) = e^{-\frac{1}{x}}e^{-\frac{1}{1-x}}$, which produces this graphic: What should $f(x,y)$ be to look like a 'hill', i.e. $f(x)$ spinned about vertical axis?
0
votes
1answer
109 views

Rotate points from one plane to another

I'm trying to create a algorithm that will rotate points given on plane 1 to plane 2. I have found two different ways of doing this. My question is ... Why are the transformation matrices different ...
0
votes
1answer
49 views

Is $M-{\hat v}^T \hat v$, positive definite (with M positive definite)?

Given a symmetric, positive definite matrix M in $\mathbb{R}^{3\times3}$, and a vector $v\in\mathbb{R}^3$. Let $\hat v$ be the skew-symmetric matrix associated with $v$: $\hat v = \begin{bmatrix} ...
0
votes
0answers
33 views

Rotating points from one plane to another plane

I'm trying to create a function that will rotate points given on plane 1 to plane 2. I have found two different ways of doing this. The attached spreadsheet shows the two different ways as Solution ...
1
vote
1answer
44 views

Compute the area defined by four non-planar points

Say we have 4 non-planar points in a 3D space (but preferably it should work in any dimension, so no cross products), $a,b,c,d$, and these points define a non-flat area. A point on that area may be ...
0
votes
0answers
11 views

aligning a matrix to reference matrix

Assuming X$_0$ as a matrix which represent some sort of transformation between TWO different coordinate system. Now, as a function of time the matrix which has three column vectors evolves in to X'. ...
2
votes
1answer
33 views

The line $\frac{x+6}{5}=\frac{y+10}{3}=\frac{z+14}{8}$ is the hypotenuse of an isosceles right angled triangle whose opposite vertex is $(7,2,4)$

The line $\dfrac{x+6}{5}=\dfrac{y+10}{3}=\dfrac{z+14}{8}$ is the hypotenuse of an isosceles right angled triangle whose opposite vertex is $(7,2,4)$.Find the equation of the remaining sides. My ...
2
votes
0answers
48 views

Prove that planes $AOA',BOB'$ and $COC'$ pass through the line $\frac{x}{l_1+l_2+l_3}=\frac{y}{m_1+m_2+m_3}=\frac{z}{n_1+n_2+n_3}$

$O$ is the origin and lines $OA,OB$ and $OC$ have direction cosines $l_1,m_1,n_1;l_2,m_2,n_2;l_3,m_3,n_3$ respectively.If lines $OA',OB'$ and $OC'$ bisect angles $BOC,COA$ and $AOB$,respectively,prove ...
1
vote
1answer
27 views

Minimal definition of a Platonic Solid

I searched in Google for the definition of Platonic solid, and I found: A platonic solid is a polyhedron all of whose faces are congruent regular polygons, and where the same number of faces ...
1
vote
1answer
27 views

If the projections of $OA$ and $OB$ on the plane $z=0$ make angles $\phi_1$ and $\phi_2$,respectively,with the $x-$axis

$OA,OB,OC,$ with $O$ as origin, are three mutually perpendicular lines whose direction cosines are $l_1,m_1,n_1;l_2,m_2,n_2$ and $l_3,m_3,n_3$ respectively. If the projections of $OA$ and $OB$ on the ...
1
vote
1answer
67 views

How to draw the 3d planes?

The equations for planes I have are $x=0$, $x=1$, $y=0$, $y=1$, $z=0$, $z=1$ but these to me look like equation of the lines. Apparently, they form a cube in 3d coordinates. Is it possible use some ...
1
vote
2answers
37 views

Prove that for all values of $\lambda$ and $\mu,$ the two planes intersect on the same line.

Prove that for all values of $\lambda$ and $\mu,$ the planes $\frac{2x}{a}+\frac{y}{b}+\frac{2z}{c}-1+\lambda(\frac{x}{a}-\frac{2y}{b}-\frac{z}{c}-2)=0$ and ...
2
votes
1answer
24 views

Show that there is a common line of intersection of the three given planes.

Let $x-y\sin\alpha-z\sin\beta=0,x\sin\alpha-y+z\sin\gamma=0$ and $x\sin\beta+y\sin\gamma-z=0$ be the equations of the planes such that $\alpha+\beta+\gamma=\frac{\pi}{2}$,(where ...
0
votes
1answer
42 views

The new position of $O,$ when triangle is rotated about side $AB$ by $90^\circ$ can be

Consider the triangle $AOB$ in the $xy$-plane where $A\equiv(1,0,0);B\equiv(0,2,0);$ and $O(0,0,0)$.The new position of $O,$ when triangle is rotated about side $AB$ by $90^\circ$ can be ...
0
votes
0answers
32 views

3d collsion rig math

I'm in quite the bind. The end result I'm looking for is to create a finger rig with collision detection. This will be done in a 3d app. The diagrams are acting as a basic visual display. B1 is ...
0
votes
1answer
31 views

Method of finding Arc length parameterization of a 3d curve

r(t) = cos^3 t i + sin^3 t j; 0 < t < pi/2. r'(t) = -3cos^2 t sin t + 3 sin^2 t cos t ||r'(t)|| = 3 sin t cos t Now to find the arc length parameterization, we need S = integration from t0 ...
0
votes
1answer
19 views

A parallelopiped is formed by planes drawn through the points $(1,2,3)$ and $(9,8,5)$ parallel to the coordinate planes

A parallelopiped is formed by planes drawn through the points $(1,2,3)$ and $(9,8,5)$ parallel to the coordinate planes then which of the following is not the length of an edge of this rectangular ...
0
votes
1answer
23 views

A rod of length $2$ units whose one end is $(1,0,-1)$ and the other end touches the plane $x-2y+2z+4=0$

A rod of length $2$ units whose one end is $(1,0,-1)$ and the other end touches the plane $x-2y+2z+4=0,$ then find the center of the region which the rod traces on the plane. The rod sweeps out the ...
0
votes
0answers
137 views

Find the equation of the plane which bisects that angle between the given planes which is acute and which contains the origin.

Consider the planes $3x-6y+2z+5=0$ and $4x-12y+3z=3$.Find the equation of the plane which bisects that angle between the given planes which is acute and which contains the origin. The two bisectors ...
1
vote
1answer
51 views

If the shortest distance between the skew lines $AB$ and $CD$ is $8$ ,find the volume of the tetrahedron.

Given a tetrahedron $ABCD$ with $D$ at the top and $AB=12,CD=6$.If the shortest distance between the skew lines $AB$ and $CD$ is $8$ and the angle between them is $\frac{\pi}{6}$,then find the volume ...
0
votes
1answer
27 views

Segments joining each vertex with the centroid of the opposite face are concurrent at the point $P$.Find the position vector of $P$

$OABC$ is a tetrahedron where $O$ is the origin.Position vectors of its angular points $A,B$ and $C$ are $\vec{a},\vec{b}$ and $\vec{c}$ respectively. Segments joining each vertex with the centroid of ...