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frustum

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frustum
frustum (ˈfrʌstəm) Pl. -a, -ums. Also erron. 7–9 frustrum. [a. L. frustum piece broken off.] 1. Math. The portion of a regular solid left after cutting off the upper part by a plane parallel to the base; or the portion intercepted between two planes, either parallel or inclined to each other.1658 Si... Oxford English Dictionary
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Frustum
A right frustum is a right pyramid or a right cone truncated perpendicularly to its axis; otherwise, it is an oblique frustum. The viewing frustum in 3D computer graphics is a virtual photographic or video camera's usable field of view modeled as a pyramidal frustum. wikipedia.org
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Frustum (disambiguation)
It may also refer to: Frustum (aerospace), a kind of payload fairing Frustum (computer graphics), the three-dimensional region visible on the screen Mount Frustum, a landform in Antarctica wikipedia.org
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A frustum is made by removing a small cone from a large cone as shown in the diagram. this the question can someone give me a step by step answer and explanation on how to do this question
Calculate the mass of the big cone first. It is $m=\frac{6^2\cdot\pi\cdot 15\cdot2.5}{3}$. The proportion between the big cone and small one is $\frac{1}{3}$ so the mass of the small cone is $m\cdot (\frac{1}{3})^3$ Finally, your answer is $m(1-(\frac{1}{3})^3)$
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Mount Frustum
Mount Frustum () is a large pyramid-shaped table mountain, high, standing between Mount Fazio and Scarab Peak in the southern part of Tobin Mesa, in Victoria The topographical feature was so named by the northern party of the New Zealand Geological Survey Antarctic Expedition, 1962–63, for its frustum-like shape wikipedia.org
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Volume of a frustum given the bottom radius and the top cone height. > A cone with base radius 12 cm is sliced parallel to its base, as shown, to remove a smaller cone of height 15 cm. If the height of the smaller con...
For the height of the bigger cone: We have $h=15 = \frac{3}{4}H \implies H = 20\text {cm}$ ![enter image description here]( $$\tan z = \frac{r}{h} = \frac{R}{H}$$ We have $R = 12, H = 20 , h = 15 \text{ (all in cm) } \implies r = \frac{R}{H}h = \cdots$ Now the height of the frustrum is $H-h = \cdots...
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What is the height of the frustum? > A sector of an annulus has a central angle of $θ$ and a thickness of $λ$. It is curved in such a manner that it forms a frustum of a cone without overlapping. > Find the height ...
If one creates a conical frustum out of the sector of the annuli then the said radii will have to be calculated.
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Radius of one of a conical frustum's circular planes, given the other's radius, the volume, and the angle? I'm trying to find the radius of the larger of the two circular planes of a frustum of a right circular cone. ...
Notice in the given figure, consider right triangles The normal height of the smaller cone (cap of the frustum) $$=r\cot\alpha$$ Volume of smaller cone radius $r$ & normal height $r\cot\alpha$ $$V_1=\frac{1}{3}\pi r^2(r\cot\alpha)=\frac{1}{3}\pi r^3\cot\alpha$$ The normal height of the larger cone (frustum
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calculate base and height frustum I would like to find a way to calculate the height (h1) and base (r2) of the frustum knowing it has the same volume than the underlying cone and the angles are the same. I got to a 3...
First we note that, since we have the small gray cone, which is part of the larger cone formed when appending the frustrum, we have that $$ \frac{h+h_1}{r_2} = \frac{h}{r} = 5$$ Next, we relate the volumes as follows: \begin{align} V_{\text{little cone}} &= V_{\text{frustrum}} \\\ &= V_{\text{big co...
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视锥体剔除（Frustum Culling）算法详解 - 知乎 - 知乎专栏
三、由透视投影矩阵计算平面方程. 我们接下来的目标，就是使用 projectionMatrix 来构建这视锥体平面的方程表达式。. 首先我们来回顾下，透视投影矩阵的用处是什么。. 利用透视投影矩阵与某个点（p）的齐次坐标相乘，我们可以得到一个半NDC坐标（ p^ {'} ），即 ...
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Three Methods to Extract Frustum Points - CodeAntenna
http://donw.io/post/frustum-point-extraction/ThreeMethodstoExtractFrustumPointsGettingfrustumpointsinworld-spacecanbeuse...,CodeAntenna ...
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How to calculate top base area with bottom base area and height of frustum? I have the following frustum The bottom base area $A_1$ is known, the top base area $A_2$ is unknown. We know this about the frustum We k...
You need some other information to calculate top base area. Let $d_1$ and $d_2$ be the lengths of upper and lower base diagonals. We have $d_2=d_1-2h/\tan a$ and the bases are similar, so that: $$ {A_2\over A_1}=\left({d_2\over d_1}\right)^2= \left(1-{2h\over d_1\tan a}\right)^2. $$ As you can see, ...
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Surface Area of Cone (And Solid of Revolution in General) From my understanding, a cone/frustum is a stack of circles with radius $r(h)$, $r$ being a linear function, and h the height. **Cone** : The surface area o...
The surface area of a cone is the base surface area (πr^2) and the slanted surface put together. The slanted area flattened looks like an iscosele triangle with a curved base with the identical edges. The straight edges is the slanted height, and the curved edge is the circumference of the base of t...
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Is it possible to determine the left/right plane equations of a frustum, given the near plane? If I am given four vertex points of the near plane that results from cutting the head of a pyramid off, is it possible to ...
* You have a point $P =\begin{pmatrix} x \\\ y \\\ z \end{pmatrix}$ in your 3d scene. Add a $1$ to get $P' = \begin{pmatrix} x \\\ y \\\ z \\\ 1 \end{pmatrix}$. * Multiply $P'$ with the projection matrix $\scriptstyle\begin{pmatrix} 1 & 0 & 0 & 0 \\\ 0 & 1 & 0 & 0 \\\ 0 & 0 & 1 & 0 \\\ 0 & 0 & 1 & -...
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Volume of a frustum SE users I was given the problem: > Find the volume of a frustum of a right circular cone with height h, lower base radius R, and top radius r. My working looks a bit too complicated and comes o...
If you first simplify your expression for $x$, you get $\displaystyle x=\frac{(R-r)(\frac{Rh}{R-r}-y)}{h}=R-\frac{R-r}{h}y,\;\;$ and then $\displaystyle V=\pi\int_{0}^{h}(R^2-\frac{2R(R-r)}{h}y+\frac{(R-r)^2}{h^2}y^2) \;dy$ $\;\;\;\displaystyle=\pi\left[R^2h-\frac{R(R-r)}{h}\cdot h^{2}+\frac{(R-r)^2...
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