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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2answers
21 views

What is the length of one turn along the axis in strip winding?

In strip winding of a cylindrical surface like this What is the length of one turn along the axis? Or what is the distance between two similar points on consecutive turns along the axis of ...
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1answer
27 views

How to minimize the surface area taken by a cylinder?

In my math class, we are working on Geometric Optimization problems. We have to create an equation, and then solve for one variable, in terms of another variable. Then, using an expression, we find ...
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2answers
26 views

How to find if the point lies in which half of the tangent plane to a sphere?

Let $S$ be the sphere $$ x^2 + y^2 + z^2 = 14$$ Equation of tangent plane to $S$ at the point $P(1, 2, 3)$ is $$ \quad \quad x+2y+3z-14=0 $$ This plane divides the whole $3-D$ plane in $2$ halves . ...
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4answers
68 views

How to find an angle between two sides of cube?

Given $\text{Cube}\ ABCDA_1B_1C_1D_1$ Find the angle between $AB_1$ and $BD_1$ Usually I will find a parallel line which has common point with the other line, however I can't find such line in this ...
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0answers
18 views

Making a Net from a 2D Image

I'm trying to find the volume of the illustration Fig.1, I've taken a scale reference from the medium diameter of a strawberry and I’ve applied this scale to the remaining sides of the shape. Fig.1 is ...
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1answer
27 views

If a plane contains one line and intersects another one elsewhere, then the two lines are not coplanar

The straight line $a$ lies in the plane $\alpha$ , the straight line $b$ intersects $\alpha$ in point $M$. If $M$ doesn't belong to the $a$ prove that there isn't plane which contains the two straight ...
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0answers
18 views

Points in half space of tangent to a sphere

Given a sphere centered at the origin, with radius R, I want to find a point on the sphere such that the tangent to the sphere at that point divides the plane into 2 half spaces, such that the ...
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1answer
23 views

Calculate position of object rotating around an axis

I have the value θ with range [0, 360] of the object rotating about the y-axis pictured below. Given a certain radius ...
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1answer
32 views

Calculating a coordinate of a triangle on a 3D plane.

I've got stuck on quite a simple problem and not sure how to proceed. I have an unknown plane and it contains a point $M(5, 2, 0)$ in it. I also have a point $P(6, 1, -1)$ (distance to the plane is ...
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1answer
46 views

How to check if a 3 dimensional point lies in a Polygon with 4 vertices

Can anyone provide an equation to this problem? Given that I have a 3 dimensional polygon that consist of 4 vertices, how do I check if pointX lies inside that polygon?
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0answers
33 views

Producing a 3D Net from a 3d inspired image

Producing a 3D Net from a 2D Image I'm trying to find the volume of the illustration, I've taken reference from the medium size of a strawberry's diameter, I've applied this scale to the remaining ...
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1answer
61 views

Pove that the angle between planes in which origin lies is acute if $a_1a_2+b_1b_2+c_1c_2<0$

Suppose we have two planes $$a_1x+b_1y+c_1z+d_1=0$$ and $$a_2x+b_2y+c_2z+d_2=0$$ where $d_1,d_2 >0 \ or \ <0$ then prove that the angle between planes in which origin lies is acute if ...
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1answer
62 views

Finding points along a catenary curve

As I am no mathematician, I have been struggling to find an equation to accurately predict points spaced along a curve separated by distance d. Given two points in 3 dimensional space, assume a string ...
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1answer
52 views

Center of Arc with Two Points, Radius, and Normal in 3D

I'm struggling to get the math to work out on this. I need to derive an alorithm for a program where I'm representing geometric entities. In this case, it's an arc. I would like to create the arc ...
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1answer
36 views

World to screen

I tried this: I have 2 players in a game (Cod 4). I read X, Y, Z and store them in: ...
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0answers
12 views

How to graph polygon rising at an angle in 3D space from the origin of the coordinate axes with shaded region on the $x$-$y$ plane?

I am trying to obtain a graph just like this one that visually shows that an objective function is maximised in z-direction at a certain point and where the “ground” of the graph is the $x$-$y$ ...
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1answer
39 views

How to tumble a camera about a point

I'm trying to implement camera tumbling as described by this document. I have a camera that defines a view position and orientation. Additionally, there is a center of interest, which is a distance ...
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1answer
28 views

How to represent 2D lines (i.e. on $x$ and $y-axis$) on a 3D graph using either Cartesian ($z=f(x,y)$) or Parametric $(x,y,z)=f(u,v)$

How to represent 2D lines (i.e. on $x$ and $y-axis$) on a 3D graph using either Cartesian ($z=f(x,y)$) or Parametric $(x,y,z)=f(u,v)$ Hi, I've been working on a Simplex problem and would like to ...
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1answer
22 views

Transform matrix to scale away from/towards an arbitrary plane in 3D space

I'm not entirely sure if this belongs in Mathematics or GameDev. I'm trying Mathematics first, so please let me know if it's in the wrong place. In 3D space, I have a plane ...
2
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2answers
63 views

How to prove that there can be infinite lines intersecting 3 skewed lines?

Few days back,I learnt somewhere in Mathematics Stack Exchange (don't exactly remember the question) that there can be infinite lines intersecting 3 skewed lines.But I'm not able to visualize or prove ...
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1answer
23 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 ...
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0answers
36 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: ...
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4answers
55 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. ...
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2answers
51 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 ...
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1answer
37 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 ...
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1answer
25 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
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3answers
126 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 ...
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0answers
17 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 ...
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0answers
24 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 ...
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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 ...
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2answers
42 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 ...
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0answers
39 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 ...
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1answer
23 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 ...
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2answers
33 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.
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2answers
26 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 ...
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0answers
22 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 ...
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1answer
19 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
33 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 ...
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0answers
10 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 ...
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0answers
22 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 $ ...
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0answers
23 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 ...
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1answer
21 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 ...
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0answers
19 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 ...
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1answer
16 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 ...
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1answer
80 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 ...
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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 ...
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0answers
11 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 ...
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2answers
25 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 ...
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0answers
14 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 ...
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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?