#computationalgeometry

[ianfulgar]

The architectural form evokes a vibrant computational bloom, with each petal extending outward from a central core. This configuration achieves harmony through the repetition of defined parameters, highlighting rhythm and consistency. The illuminated core at the center of the pavilion conveys a dynamic sense of activation and energy, reflecting the innovative and exploratory nature of artificial intelligence in design. The structure integrates organic growth with technological sophistication, fostering curiosity and engagement.

[philearning]

INTRODUCTION TO ALGORITHMS - The third edition has been revised and updated throughout. It includes two completely new chapters, on van Emde Boas trees and multithreaded algorithms, and substantial additions to the chapter on recurrences (now called “Divide-and-Conquer”). Self-direct your studies with an exhaustive range of academic Textbooks Collection of PHI Learning Buy Now: https://bit.ly/3gN4HtA #Algorithms #Engineering #BinarySearchTrees #ComputationalGeometry #GraphAlgorithms https://www.instagram.com/p/CBBjpBeHxF1/?igshid=pt4jnersyhfj

[sinamostafavi]

Bench to wall to..., 1 to 10 tight and seamless 3D printed prototype with varied interlocked components #Workinprogress result of our design computation to materializations workshop #designstudio #d2rp #robotsinarchitecture #bkcity #designtoproduction #roboticbuilding #SinaMostafavi #AndreaCosta #OscarBorgström #RebeccaLopesCardozo #TheonaKessaris #architecture #nextarch #superarchitects #porosity #urbanfurniture #prototyping #architecturalrobotics #designresearch #3dprinting #3dprint #ultimaker #additivemanufacturing #computationaldesign #computationalgeometry (at Amsterdam, Netherlands)

[emrecangulay-blog]

A formal definition to computational geometry given by Robin Forrest in 1971 as 'computer-based representation, analysis, synthesis (design) and computer-controlled manufacture of two and three dimensional shapes.

[amazingdraft]

Angle between three points

Once I had to write some code (C++) related to computational geometry involving triangles and meshes (the goal was a Delaunay triangulation). One of the first codes was to find the angle given three points.

The main idea was: read three points (six pair of coordinates) and calculate the internal angle of this triangle formed by this three points.

So, the question is: how to find the angle between two vectors? A little math is needed here.. specifically in the dot product, which can be written as:

,

where θ is the angle formed by the vectors |A| and |B| their magnitude:

Now we can find θ:

To find α, β and θ of the first Figure, we have to calculate the magnitude of the three vectors:

Finally, the angles:

Remember: these angles are in radian. To pass to degree we have to multiply by 180 and divide by π.

Here is the C/C++ code:

#include <stdio.h> #include <math.h> double getMagnitude(int x1, int x2, int y1, int y2) { double aux = (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2); return sqrt(aux); } double getAngle(int x1, int x2, int x3, int y1, int y2, int y3, double V1, double V2) { double aux = ((x2-x1)*(x3-x1) + (y2-y1)*(y3-y1))/(V1*V2); return acos(aux); } double rad2deg(double angle) { return angle*180/3.1415; } int main(int argc, char *argv[]) { // Coordinates int x1=10, y1=10; int x2=50, y2=10; int x3=10, y3=40; // STEP 1: Magnitude of vectors A, B and C double A = getMagnitude(x2,x3,y2,y3); double B = getMagnitude(x3,x1,y3,y1); double C = getMagnitude(x1,x2,y1,y2); // STEP 2: Angles alpha(C-B) beta(A-B) theta(C-A) double alpha = getAngle(x1,x2,x3,y1,y2,y3,C,B); double beta = getAngle(x3,x2,x1,y3,y2,y1,A,B); double theta = getAngle(x2,x1,x3,y2,y1,y3,C,A); // STEP 3*: Radian to degree alpha = rad2deg(alpha); beta = rad2deg(beta); theta = rad2deg(theta); printf("alpha: %lf\nbeta: %lf\ntheta: %lf\n",alpha,beta,theta); }

You should get this values: