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Geometry, Surfaces, Curves, Polyhedra

Geometry, Surfaces, Curves, Polyhedra
Notes on polygons and meshes Includes Surface (polygon) simplification, Clipping a polygonal facet with an arbitrary plane, Surface Relaxation and Smoothing of polygonal data, Mesh crumpling, splitting polygons, two sided facets, polygon types, tests for clockwise and concavity, clipping line to polygons, area of a 3D polygon, area of general polygons, determining inside/outside test, intersection of a line and a facet, Eulers numbers. Notes on points, lines and planes Includes calculations for the distance between points, lines and planes. The intersection between 2 lines in 2D and 3D, the intersection of a line with a plane. The intersection of two and three planes. The only thing that saves us from the bureaucracy is its inefficiency. Notes on circles, cylinders and spheres Includes equations and terminology. Transformations and projections Methods for mapping points on a spherical surface onto a plane, stereographic and cylindrical (including Mercator) projections. Other ...

http://paulbourke.net/geometry/

Related:  Generative designMATH / GEOMETRYA RANGER AUSSI

Fabrication Grasshopper: Parametric CurvesThis module covers the basic parametric properties of curves along with common grasshopper methods for evaluating and dividing curves. ARCH 598 Summer 2011information >> n-formations FABRICS // LATTICES // FIELDSThis course is designed to introduce and explore computational design, algorithmic thinking, and digital manufacturing–both: the larger ramifications that emerging digital technologies and ideas are having architectural theory via readings, discussions, presentations; and the practical application of these ideas and tools through a series of hands-on, iterative modeling and fabrication assignments. ARCH 581/498 : Fall 2010Digital Design + Fabrication Foundations I Grasshopper: Surface to Planar TrianglesGrasshopper : Surface to Planar Triangles : Fabrication Layout of Planar Components

One man's Funnies: Mathematical equations of love, heart, penis and the boomerang Love Love is complicated. But the mathematics of it is very simple: - It starts with "I love you" where "I love" is a constant, and "you" is a variable. - Later on, it is: 1 + 1 = 1 - And later still: 1 + 1 >= 3 Any questions? Now, let us explore the mechanics of love. Heart RHINO: GRASSHOPPER DEFINITIONS - RHINO / GH This definition was developed for my final thesis project to generate a louver system based on functional requirements within the building. The performance was then tested in Ecotect. A large part of my thesis design involved invertible arena seating with many moving parts. I used Grasshopper as a means to develop the seating testing clearances, site lines, and many other variables. This definition looks at taking any curved surface, and generating weaving geometry across it.

Spirographs and the third dimension The basic geometric ideas are straight lines and circles. The famous compass and straight edge. There is a great deal that can be done with just these, but what if you want something more complex? Spirographs are a very simple idea, let one circle run around a second. Grasshopper Modules - Proxy Wiki From Phylogenesis, FOA 2003 The following Grasshopper modules were created in consultation with FOA's Phylogenesis, in particular the taxonomy of forms found at the conclusion of the book. Grasshopper is an exciting and evolving modeling platform - the following examples attempt to develop a range of geometric examples to explore its form-making potentials. Andrew Payne, a GSAPP alum, has created a comprehensive primer on Grasshopper that can be found here.

Download Please note that Scriptographer currently still is beta software. By downloading it from this page, you agree to these terms: The Scriptographer software is provided to you "as is", and we make no express or implied warranties whatsoever with respect to its functionality, operability, or use, including, without limitation, any implied warranties of merchantability, fitness for a particular purpose, or infringement. We expressly disclaim any liability whatsoever for any direct, indirect, consequential, incidental or special damages, including, without limitation, lost revenues, lost profits, losses resulting from business interruption or loss of data, regardless of the form of action or legal theory under which the liability may be asserted, even if advised of the possibility or likelihood of such damages. After downloading, please read the installation instructions. Scriptographer Version 2.9 Please note:

Heart Curve What is the Heart Curve? If you speak about a heart, you rather mean the heart figure than the heart shaped curve. Drawn Heart Curves topMethod 1 Method 2 Tutorial 3 - Reciprocal Systems - AAET picture: arup agu This tutorial will show how a reciprocal system can be constructed using Rhino, Grasshopper as design environment to inform a physical model. Download Tutorial as pdf - workshopsafd8-digitalmaterialandfabrication-tut3-reciprocal Download Rhino and Grasshopper file example of the GH definition colouring sticks by length from Wolfram MathWorld Lissajous curves are the family of curves described by the parametric equations sometimes also written in the form They are sometimes known as Bowditch curves after Nathaniel Bowditch, who studied them in 1815.

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