Geometric algorithms

Geometric primitive

In vector computer graphics, CAD systems, and geographic information systems, geometric primitive (or prim) is the simplest (i.e. 'atomic' or irreducible) geometric shape that the system can handle (draw, store). Sometimes the subroutines that draw the corresponding objects are called "geometric primitives" as well. The most "primitive" primitives are point and straight line segment, which were all that early vector graphics systems had. In constructive solid geometry, primitives are simple geometric shapes such as a cube, cylinder, sphere, cone, pyramid, torus. Modern 2D computer graphics systems may operate with primitives which are curves (segments of straight lines, circles and more complicated curves), as well as shapes (boxes, arbitrary polygons, circles). A common set of two-dimensional primitives includes lines, points, and polygons, although some people prefer to consider triangles primitives, because every polygon can be constructed from triangles. All other graphic elements are built up from these primitives. In three dimensions, triangles or polygons positioned in three-dimensional space can be used as primitives to model more complex 3D forms. In some cases, curves (such as Bézier curves, circles, etc.) may be considered primitives; in other cases, curves are complex forms created from many straight, primitive shapes. (Wikipedia).

Geometric primitive
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What is a geometric mean

Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.

From playlist Geometry - GEOMETRIC MEAN

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Geometric Algebra - The Matrix Representation of a Linear Transformation

In this video, we will show how matrices as computational tools may conveniently represent the action of a linear transformation upon a given basis. We will prove that conventional matrix operations, particularly matrix multiplication, conform to the composition of linear transformations.

From playlist Geometric Algebra

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What is the definition of a geometric sequence

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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Multisets and a new framework for arithmetic | Data Structures Math Foundations 187

Here we go back to the first videos in this series and recast that discussion in a more solid direction by utilizing our understanding of multisets. The crucial point is to define what a natural number is in a clear way. This issue is far more subtle than is generally acknowledged. For u

From playlist Math Foundations

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How to determine the rule for a geometric sequence given two values

👉 Learn how to write the explicit formula for a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multi

From playlist Sequences

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Geometric Algebra - Linear Transformations, Outermorphism, and the Determinant

In this video, we will review some basic concepts from linear algebra, such as the linear transformation, prove important theorems which ground matrix operations, extend the linear transformation on vectors to higher-graded elements to bivectors and trivectors, and define the determinant o

From playlist Geometric Algebra

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Learn how to find the geometric mean between two numbers

Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.

From playlist Geometry - GEOMETRIC MEAN

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Reconsidering natural numbers and arithmetical expressions | Data structures Math Foundations 185

It is time to turn our gaze back to the true foundations of the subject: arithmetic with natural numbers. But now we know that the issue of "What exactly is a natural number?" is fraught with subtlety. We adopt a famous dictum of Errett Bishop, and start to make meaningful distinctions bet

From playlist Math Foundations

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Learn to write the explicit formula for the geometric sequence

👉 Learn how to write the explicit formula for a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multi

From playlist Sequences

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Live CEOing Ep 70: Geometry in Wolfram Language

Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Geometry in the Wolfram Language.

From playlist Behind the Scenes in Real-Life Software Design

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Counting embedded curves in symplectic 6-manifolds - Aleksander Doan

Symplectic Dynamics/Geometry Seminar Topic: Counting embedded curves in symplectic 6-manifolds Speaker: Aleksander Doan Affiliation: Columbia University Date: February 03, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

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Frank Gounelas : Rational curves on K3 surfaces

Bogomolov and Mumford proved that every complex projective K3 surface contains a rational curve. Since then, a lot of progress has been made by Bogomolov, Chen, Hassett, Li, Liedtke, Tschinkel and others, towards the stronger statement that any such surface in fact contains infinitely many

From playlist Algebraic and Complex Geometry

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Lecture 13: Spatial Data Structures (CMU 15-462/662)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/

From playlist Computer Graphics (CMU 15-462/662)

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Geometry of best Approximations by Uri Shapira

DISCUSSION MEETING STRUCTURED LIGHT AND SPIN-ORBIT PHOTONICS ORGANIZERS: Bimalendu Deb (IACS Kolkata, India), Tarak Nath Dey (IIT Guwahati, India), Subhasish Dutta Gupta (UOH, TIFR Hyderabad, India) and Nirmalya Ghosh (IISER Kolkata, India) DATE: 29 November 2022 to 02 December 2022 VE

From playlist Ergodic Theory and Dynamical Systems 2022

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Automated Planar Geometry

We present updates to the automated geometric functionality of the Wolfram Language introduced in Version 12, including new functionality for automated geometric reasoning and for creating GeometricScene objects.

From playlist Wolfram Technology Conference 2022

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Hodge theory and derived categories of cubic fourfolds - Richard Thomas

Richard Thomas Imperial College London September 16, 2014 Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with K3s associated to them at the le

From playlist Mathematics

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How to write the explicit formula of a geometric sequence given two terms of

👉 Learn how to write the explicit formula for a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multi

From playlist Sequences

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Holomorphic Curves and the ADHM Vortex Equations by Aleksander Doan

PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie

From playlist Vortex Moduli - 2023

Related pages

Ellipse | Bézier curve | Interpolation | Polygonal chain | Line (geometry) | Dimension | Curve | Non-uniform rational B-spline | Cubic Hermite spline | Pyramid (geometry) | Torus | Simplex | Surface | Triangle mesh | Polygon mesh | Point (geometry) | Line segment | Triangle strip | Cartesian coordinate system | Constructive solid geometry | Polygon | Polyhedron | Sphere | Triangulated irregular network | Computational geometry | Geometry | Triangle | Circle