Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 9x 9x 9x 9x 9x 9x 9x 9x 9x 9x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 2x 2x 2x 2x 2x 2x | /**
* @fileOverview
* Defines various geometry related helper functions
*/
import {
apply as matrixApply,
sum as matrixSum,
divide as matrixDivide,
size,
index,
subset,
det,
dotMultiply
} from 'mathjs';
/**
* computes centroid given a set of points
* @param points
* @returns centroid of 'points'
*/
export function getCentroid(points: number[][]) {
const pointsSize = size(points).valueOf() as Array<number>;
const numPoints = pointsSize[0];
const pointsSum = matrixApply(points, 0, matrixSum);
const centroid = matrixDivide(
pointsSum,
numPoints
).valueOf() as Array<number>;
return centroid;
}
/**
* Matrix denotes the basis vectors of the linear space. The orientation of the
* basis vector should not change after rotating. So after computing rotation
* matrix, we should check if the orientation is the same as before. Sign of
* determinant of the matrix gives the orientation of the basis vectors.
* Therefore, if the sign of the determinant is negative, we multiply the third
* column of rotation matrix by -1, so that the orientation changes and sign of
* determinant becomes positive again.
* @param rotationalMatrix
* @returns 3x3 matrix
*/
export function checkOrientation(rotationalMatrix: number[][]) {
const determinant = det(rotationalMatrix);
if (determinant < 0) {
const thirdColumn = subset(rotationalMatrix, index([0, 1, 2], 2));
rotationalMatrix = subset(
rotationalMatrix,
index([0, 1, 2], 2),
dotMultiply(thirdColumn, -1)
);
}
return rotationalMatrix;
}
|