The curved point-normal triangle, in short PN triangle, is an interpolation algorithm to retrieve a cubic BΓ©zier triangle from the vertex coordinates of a regular flat triangle and normal vectors. The PN triangle retains the vertices of the flat triangle as well as the corresponding normals. It was first introduced by Saul Kato in 1999 and later independently by A. Vlachos et al. in 2001 and is primarily used in the field of computer graphics. The usage of the PN triangle enables the visualization of triangle based surfaces in a smoother shape at low cost in terms of rendering complexity and time. (Wikipedia).
Determine points on a unit circle using special triangles
π Learn about the points on the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersec
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
Overview of points lines plans and their location
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
What are the points on a unit circle by 45 degrees
π Learn about the points on the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersec
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
Determining the Distance Between a Plane and a Point
http://mathispower4u.yolasite.com/
From playlist Equations of Planes and Lines in Space
Name the opposite rays in the given figure
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Code-It-Yourself! 3D Graphics Engine Part#2 - Normals, Culling, Lighting & Object Files
In Part #2 of this series, I setup more fundamentals, including triangle culling if it can't be seen, surface illumination and a quick way to import Object files from 3D modelling software. Source: https://github.com/OneLoneCoder/Javidx9/tree/master/ConsoleGameEngine/BiggerProjects/Engine
From playlist Code-It-Yourself!
Lecture 14: Discrete Surfaces (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Code samples derived from work by Joey de Vries, @joeydevries, author of https://learnopengl.com/ All code samples, unless explicitly stated otherwise, are licensed under the terms of the CC BY-NC 4.0 license as published by Creative Commons, either version 4 of the License, or (at your o
From playlist OpenGL
Code-It-Yourself! 3D Graphics Engine Part #3 - Cameras & Clipping
Phew, it's a long one but I feel necessary to get this series moving. This video describes how to implement cameras and clipping planes in a 3D engine. In addition, I derive the look at and point at matrices, typically used in cameras, and talk about how to clip triangles against planes in
From playlist Code-It-Yourself!
Naming the rays in a given figure
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
plot angles in standard position, coterminal angles, http://mathispower4u.wordpress.com/
From playlist Angles and Right Triangles
Joel Hass - Lecture 2 - Algorithms and complexity in the theory of knots and manifolds - 19/06/18
School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Joel Hass (University of California at Davis, USA) Algorithms and complexity in the theory of knots and manifolds Abstract: These lectures will introduce algorithmic pro
From playlist Joel Hass - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
CCSS How to Label a Line, Line Segment and Ray
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Code samples derived from work by Joey de Vries, @joeydevries, author of https://learnopengl.com/ All code samples, unless explicitly stated otherwise, are licensed under the terms of the CC BY-NC 4.0 license as published by Creative Commons, either version 4 of the License, or (at your o
From playlist OpenGL
Lecture 11: Digital Geometry Processing (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)
Lecture 17: Discrete Curvature II (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Back to normal! In this video I examine a framework to experiment with different racing lines along a parametric track. Source: https://github.com/OneLoneCoder/Javidx9/blob/master/ConsoleGameEngine/SmallerProjects/OneLoneCoder_RacingLines.cpp https://discord.gg/WhwHUMV Blog: http://www.o
From playlist Interesting Programming
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
Lecture 8: Computing Curvature
CS 468: Differential Geometry for Computer Science
From playlist Stanford: Differential Geometry for Computer Science (CosmoLearning Computer Science)
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes