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5 views

Generate X, Y, Z coordinates of 3D triangular prism with Edge Rounding

I'm trying to create an interactive 3D visualization with Python and Mayavi for inputs to an analysis program. The program accepts certain primitive shapes which it combines (constructive solid ...
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0answers
8 views

What is the distance between plane ACH and BEG from this following cube?

Given: cube ABCD.EFGH with length of its edge is r cm. What is the distance between plane ACH and BEG? Here is my attempted drawing: http://i57.tinypic.com/wgtc1.png From this picture, I take a ...
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0answers
13 views

Tip of base to edge of top

Consider a frustum of a cone. For instance that I want to get the part by cutting it from the right end tip of its base to the left end edge of its top. The part that I want to see is the part that ...
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1answer
68 views

How can the tension force be computed to test if a shape is moving or not?

Source Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be ...
3
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1answer
50 views

How to compute force on joints of a 3D structure of balls connected by rods?

Source Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be ...
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0answers
15 views

Question about relationship between line and plane in solid geometry?

Given: Cube ABCD.EFGH, with P and Q as midpoints of CG and BF respectively. What is the relationship between: a. EP and plane ABCD b. AC and plane EQPH My attempt: a. Since EP at plane ACGE ...
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1answer
30 views

Triangle inside a cylinder, surface times circumference - hard to visulize question

The surface of the triangle is $X$ and the circumfrence of the base of the cylinder is $Y$. What is the volume of the cylinder ? The answer is $XY$ but why ? If you'll take the ...
2
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1answer
44 views

Solids of Revolution - Negative volume?

So I'm to find the volume of the solid formed by the area trapped between $y = x$ and $y = \sqrt{x}$, rotated about $y = 1$ The two curves cross at y = 0 and y = 1 so they will be the upper/lower ...
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1answer
30 views

locus sections and circles--symmetry

A. Let L = {(x,y,z)|the distance from (x,y,z) to the y-axis is 6}. Describe what shape L is. So far, I have that it's a circle, but I'm not sure how to describe it fully. Would it be a circle that ...
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2answers
41 views

Use cylinder's formula for frustum (conical frustum)

I know that frustum(conical) has a formula for its volume,i.e. $\frac1 3\pi h(r^2+R^2+rR)$, but why can't we place the average of two radii into cylinder's formula: $\pi(\frac{r+R}2)^2(h)$? I need ...
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0answers
19 views

Difference between polyhedral, CSG and B-rep

I am working on the 3D object modeling project. I found objects can be represented in the form of Polyhedrol model, CSG (Constructive Solid Geometry) model, and as well as B-Rep (Boundary ...
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1answer
59 views

How will I get the volume and surface area of the sphere?

If a rectangular solid have edges, 4 cm, 5 cm and 7 cm, is inscribed in a sphere. How will I get the volume and surface area of the sphere? Do I need to get the volume of the rectangular solid and ...
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0answers
25 views

Lattice orthogonal polyhedra face-area sequences: Golyhedra?

Let $P$ be a polyhedron, all of whose vertices are at points of $\mathbb{Z}^3$, all of whose edges are parallel to an axis, with every face simply connected, and the surface topologically a sphere. ...
6
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1answer
148 views

Sum of radii of exspheres

I am interested in finding some results for tetrahedron that would be analoguous to known results for triangle. In triangle with circumradius R and inradius r, if we consider the excircles $r_i$, then ...
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1answer
62 views

Ellipse Tangents in 3D

I know that we can find the tangent of the ellipse in 2D by taking the derivative of the equation defining the ellipse. But I'm little bit confused about finding the ellipse tangent in 3D. Where the ...
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0answers
31 views

Compute the volume of a solid

I've solved this exercise and my answer contradicts the one in the back of the book. It might be a misprint but I need to be sure. The book is Apostol's Calculus vol. 1. The book says $16\sqrt3/3$, my ...
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1answer
29 views

Intersected cone, a practical problem

This is the maths representation of a problem which I have from the practice. We have an interested cone with a diameter of the base $d$, height $h$ and the angle $\alpha$ as shown on the drawing. A ...
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2answers
41 views

Point of tangency between plane and sphere

How can one find the point of tangency between a plane and a sphere in $\mathbb{R}^3$? The equations of the plane and the sphere are $x + y + z - 5 = 0$ and $(x-1)^2 + (y-2)^2 + (z+1)^2 = 3$ ...
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1answer
58 views

Find the area of the Grayed triangle Given the following Figure

Can you help me find the area of the gray triangle in the given figure. I'm having a hard time finding the base value of the triangle, I've managed to find the sides for the big triangle but not ...
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1answer
71 views

Line Drawing Using Bresenham Algorithm

Indicate which raster locations would be chosen by Bersenham’s algorithm when scan converting a line from screen co-ordinates (1,1) to (8,5). First the straight values (initial values) must be found ...
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1answer
75 views

vectors in 3D space and Right-Hand Rule

Suppose we have three vectors in 3D space. My questions are: How we check if these vectors are satisfy the right-hand rule or not. I know that it's possible to make the three vectors satisfy the ...
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3answers
69 views

Generalization of angle bisector to tetrahedron

Let $I$ be the center of the inscribed sphere of a tetrahedron $ABCD$ and let $I_A$ be the length of the line passing through $I$ from the vertex $A$ to the opposite face. I am looking for a formula ...
2
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0answers
21 views

The exact type of my 3d model

I have reconstructed vertical features (hole like objects lie on a vertical face) lie on two connected faces. To understand the situation, I say I have 2 walls with many windows and doors on ...
0
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1answer
52 views

Perspective projection onto y/z plane?

On wikipedia there is an article on 3d perspective projection onto the x/y plane. http://en.wikipedia.org/wiki/3D_projection#Perspective_projection How do I project onto the y/z plane? If i have a ...
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1answer
70 views

Icosahedron and dual dodecahedron coordinates and rotations

I'm trying to build a 20 sided die in Actionscript 3, like one in the picture. I figure the best way would be to make it out of 20 equilateral triangles rotated in 3D space. The vertices of the ...
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1answer
15 views

calculate size of faces to have similar volume of platonic solids

I need to build some prototype physical shapes of the 5 platonic solids. But the problem is that I want to make them all about the same size, so how to calculate how big should the faces of my ...
2
votes
1answer
44 views

what will be the angle at the centre?

Taken a tetrahedron of same edges, a point is taken inside it which is equidistant from all $4$ vertices, i.e if a sphere is made taking it as a centre, all the vertices will be on the sphere, now ...
2
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1answer
74 views

Disk and washer problem

I need to find the volume of the solid obtained by rotating the region bounded by the following functions: $xy = 1, y = 0, x = 1, x = 2;$ about $x = -1$ I think the outer radius of the washer is ...
5
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3answers
125 views

Which solids are characterized by their orthographic projections?

If I know the orthographic projections of a given solid in Euclidean 3-space onto the $xy$, $xz$ and $yz$ planes, under which circumstances can I reconstruct the solid based on that information alone? ...
0
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0answers
109 views

Cutting a solid torus by a plane parallel to its rotary axis

I've been interested in finding a cutting method such that the area of the cut surface is max when we cut a $3$ dimensional solid by a plane. Then, here is my question. Question : How about the ...
1
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0answers
43 views

Finding an angle in a straight pyramid

We have a straight pyramid with a square ABCD as its base and apex S. We're given the pyramid's height 8 and the angle 48 deg. between SA and SC. I've already managed to calculate the pyramid's volume ...
2
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0answers
62 views

Finding an angle in a pyramid

We have a straight pyramid with a square ABCD as its base and apex S. We're given the pyramid's height 8 and the angle 48 deg. between SA and SC. I've already managed to calculate the pyramid's volume ...
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1answer
385 views

Is there a dissection proof of the Pythagorean Theorem for tetrahedra?

Of the many nice proofs of the Pythagorean theorem, one large class is the "dissection" proofs, where the sum of the areas of the squares on the two legs is shown to be the same as the area of the ...
5
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1answer
179 views

Volume of a sphere with three holes drilled in it.

Suppose that the sphere $x^2+y^2+z^2=9$ has three holes of radius $1$ drilled through it. One down the $z$-axis, one along the $x$-axis, and one along the $y$-axis. What is the volume of the resulting ...
2
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0answers
61 views

Angle between two planes, finding the second plane

I've got a plane given by $x-y+z=0$ and a line given by $r=(0,0,a)+t(1,1,b)$. How do I find another plane that contains the line and intersects the other plane at an angle of $45^\circ$? Is ...
0
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1answer
76 views

Eigenvectors for the equation of the second degree and right-hand rule

I'm trying to find the Eigenvectors for the equation of the second degree (for example Elliptic cone). The estimated values $V_1$, $V_2$ and $V_3$ must satisfy the right-hand rule. How can we verify ...
4
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1answer
187 views

Online Math Open Contest 2 Problem 50

In tetrahedron $SABC$, the circumcircles of faces $SAB$, $SBC$, and $SCA$ each have radius $108$. The inscribed sphere of $SABC$, centered at $I$, has radius $35.$ Additionally, $SI = 125$. Let $R$ be ...
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1answer
199 views

Find the volume of the solid about y-axis, i.e. 1/(x^2+3x+2), bounds x=0, x=1

find intersection points: 1/(x^2+3x+2)=1, so x=(sqrt(5)-3)/2, x= -(sqrt(5)+3)/2 thus we have: V(volume)= Pi*integral((1)^2-(1/(x^2+3x+2)^2) from x= -(sqrt(5)+3)/2, x= (sqrt(5)-3)/2 ...
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1answer
68 views

Instrinsic definition of concave and convex polyhedron

Is it possible to distinguish a concave polyhedron from a convex one by mesurements made only on its surface, without a reference to the 3d space around it?
0
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1answer
69 views

Correcting plane parameters with the fixed azimuth angles

I am trying to reconstruct specific 3d objects such as cubes, pyramids and so on. For this, i am using point cloud data and then fitting planar surfaces for the segmented point patches. Planes ...
1
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0answers
30 views

How to fit a cuboid into a polyhedra?

I have multiple points which create a solid (polyhedra). And now I want to place a cuboid inside this solid in a way that it uses the maximum amout of space inside. Are there any solutions for this ...
2
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1answer
137 views

solid angle of polyhedron

I have an interesting thought when I draw polygon and 3D polyhedron. My question is: Can I know the number of Face, Edge, and Vertex from a given 'space angle constraint'? For example, a vertex a cube ...
1
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3answers
137 views

Surface area comparison of a solid cut in half

This was just a thought I had while driving this morning, no particular application. If you make a straight line cut through a solid object such that the resulting two pieces have the same volume, ...
2
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1answer
194 views

Prove that $S$ is a sphere.

Let $S\subset {\mathbb{R}}^3$ with the following properties: $1.$ For any line $l$: $|l\cap S|=2$ or $|l\cap S|=1$ or $|l\cap S|=0$ $2.$ For any plane $P$ $P\cap S=\text{circle}$ or $|P\cap S|=1$ ...
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1answer
137 views

Numerical computation of surface curvature

In 2 dimensions, the definition of curvature of a curve $y = y(x)$ is \begin{equation} C = \frac{y''}{(1+y'^{2})^{3/2}} \end{equation} and it is easy to estimate the curvature numerically for given ...
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2answers
186 views

get a rotation matrix from an oriented vector quicker than Euler

I'm in $R^3$ and I have a solid 3d object and a vector, I would like to rotate and orient the solid according to this vector. I found that the simplest way to do that is to use euler angles, the ...
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1answer
212 views

Surface of a sphere inside a concentric cube

Given a sphere of radius r, and a cube of unit length with the same center as the sphere, what is the surface area of the sphere that is inside the cube, when $\sqrt{2}/2 <r < \sqrt{3}/2$?
3
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0answers
111 views

Maximum length of pencil in a pencil case

What is the maximum length of an unsharpened, cylindrical pencil inside an empty rectangular pencil box? Or, in a rectangular cuboid of dimensions $x \times y \times z$, what is the maximum possible ...
2
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1answer
43 views

What's the name of each pseudo-rectangle in a spherical surface?

Consider the common surface of a spherical segment crossed with a spherical wedge. This produces a pseudo-rectangle in the sphere surface, and a perfect rectangle in a mercator projection. What's the ...
0
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1answer
128 views

Volume of a cylinder on a slope

A cylindrical water tank which is 35 feet in diameter and 105 feet in length is placed temporarily on an 18.5 degree slope. The filler is located flush with the top of the tank at midpoint. What is ...