The tag has no wiki summary.

learn more… | top users | synonyms

0
votes
0answers
116 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 ...
0
votes
1answer
161 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 ...
0
votes
0answers
118 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
votes
1answer
159 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 ...
0
votes
1answer
159 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 ...
0
votes
1answer
56 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 ...
0
votes
2answers
58 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 $(x-1)^2 + (y-2)^2 + (z+1)^2 = 3$ ...
1
vote
1answer
84 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 ...
0
votes
1answer
488 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 ...
0
votes
1answer
112 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 ...
2
votes
3answers
115 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
votes
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
votes
1answer
99 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 ...
1
vote
1answer
125 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 ...
1
vote
1answer
22 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
46 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
votes
1answer
138 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
votes
3answers
138 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? ...
1
vote
0answers
51 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
votes
0answers
111 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 ...
13
votes
1answer
800 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
votes
1answer
223 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 ...
3
votes
0answers
97 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
votes
1answer
100 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
votes
1answer
231 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 ...
1
vote
1answer
308 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 ...
1
vote
1answer
98 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
votes
1answer
99 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
vote
0answers
39 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
votes
1answer
255 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
vote
3answers
233 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
votes
1answer
225 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 $|P\cap S|=1$ ...
0
votes
1answer
304 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 ...
0
votes
2answers
246 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 ...
1
vote
1answer
273 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
votes
0answers
174 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
votes
1answer
52 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
votes
1answer
179 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 ...
4
votes
0answers
108 views

Icosahedral symmetry

Is there a clear and correct reference for full icosahedral symmetry that includes a presentation and its action on vertices, edges, and faces? The Wikipedia article for icoshedral symmetry gives ...
0
votes
0answers
150 views

how to get optimal vector, which is parallel to intersection line of many plane (Least Square way)

My idea is to construct the best optimal 3D line representing the intersection of many 3D planes. (As we know, due to fitting errors or data errors, the fitted planes might not intersect exactly ...
2
votes
0answers
150 views

Faces on a rotating cube

This one is probably a softball question, but... Fact: A cube has 6 faces Fact (unless my math is wrong): A cube that is cut in half center horizontal can be reoriented to have 18 unique faces. ...
1
vote
0answers
164 views

Creating polyhedra with playing cards

In here, George Hart gives some exciting examples on how to create polyhedra by cutting playing cards and sliding them inside one another. I was wondering if such an approach can be generalized to ...
0
votes
1answer
225 views

producing tetrahedra within a cube

A common math problem involves dividing a cube into regular and irregular tetrahedra, where the points of the cube must also be the points of the tetrahedra. A problem I'm working on seems to be ...
2
votes
3answers
781 views

What is the formula for a 3D line?

Just like we have the formula $y=mx+b$ for $\mathbb{R}^{2}$, what would be a formula for $\mathbb{R}^{3}$? Thanks.
1
vote
1answer
51 views

Help with school solid geometry

In the triangular pyramid $MABC$ all side edges equals $1$, $\angle AMB = \angle BMC = 60 ^\circ$, $\angle AMC = 45 ^\circ$. Find: 1) square of the $\triangle ABC$; 2) dihedral angle on the $AB$ ...
1
vote
0answers
66 views

Following a polyline along the surface of a polygon that is twisted

I have (hopefully) an interesting problem regarding geometry. I will also search online and in literature but I thought to pose the question here as a third resource. For my problem I need to get the ...
0
votes
1answer
218 views

least square solution for obtaining a line 3d by intersecting many planes

If I have been given 4 planes and I know only a point (just a point lie on the plane e.g. o1,o2, o3 & o4) and normal vector of each plane (n1, n2, n3 & n4). Then, by intersecting all 4 (or ...
0
votes
2answers
343 views

Analytic geometry section of cone and sphere

How to show that the cone $yz+zx+xy=0$ cuts the sphere $x^2+y^2+z^2=a^2$ in two equal circle ? I understand that the two equations taken together represent the circle. but how to go about finding the ...
4
votes
1answer
137 views

What is the minimal isoperimetric ratio of a polyhedron with $5$ vertices?

I'm asking and answering this question to provide a partial answer to this question and a comment on this answer at MO. The isoperimetric ratio $\mu$ of a solid is the ratio $A^3/V^2$, where $A$ is ...
0
votes
1answer
122 views

What is the minimum number of blocks to build this?

A rectangular solid is built using $N$ cubes of a side length of 1cm. When viewed from such an angle such that only 3 of the sides of the rectangular solid are visible, there are 231 $cm^2$ of area ...