@allmaps/transform/dist/transformation-types/Projective.js

Coordinate transformation functions

import { newArrayMatrix } from '@allmaps/stdlib';
import { BaseTransformation } from './BaseTransformation.js';
import { solveJointlySvd } from '../shared/solve-functions.js';
/**
 * 2D projective (= perspective) transformation
 *
 * For this transformations, the system of equations is solved for x and y jointly.
 *
 * See for more information:
 * Dubrofsky, Elan. "Homography estimation." Diplomová práce. Vancouver: Univerzita Britské Kolumbie 5 (2009).
 * https://citeseerx.ist.psu.edu/doc/10.1.1.186.4411
 * https://www.cs.ubc.ca/sites/default/files/2022-12/Dubrofsky_Elan.pdf
 */
export class Projective extends BaseTransformation {
    coefsArrayMatrices;
    weightsArrays;
    constructor(sourcePoints, destinationPoints) {
        super(sourcePoints, destinationPoints, 'projective', 4);
        // Construct two Nx9 Matrix projectiveCoefsMatrix
        // −x0 −y0 −1  0   0   0  x'0x0 x'0y0 x'0
        // ...
        // 0   0   0   −x0 −y0 −1 y'0x0 y'0y0 y'0
        // ...
        this.coefsArrayMatrices = [
            newArrayMatrix(this.pointCount, 9, 0),
            newArrayMatrix(this.pointCount, 9, 0)
        ];
        for (let i = 0; i < this.pointCount; i++) {
            this.coefsArrayMatrices[0][i][0] = -sourcePoints[i][0];
            this.coefsArrayMatrices[0][i][1] = -sourcePoints[i][1];
            this.coefsArrayMatrices[0][i][2] = -1;
            this.coefsArrayMatrices[0][i][3] = 0;
            this.coefsArrayMatrices[0][i][4] = 0;
            this.coefsArrayMatrices[0][i][5] = 0;
            this.coefsArrayMatrices[0][i][6] =
                destinationPoints[i][0] * sourcePoints[i][0];
            this.coefsArrayMatrices[0][i][7] =
                destinationPoints[i][0] * sourcePoints[i][1];
            this.coefsArrayMatrices[0][i][8] = destinationPoints[i][0];
            this.coefsArrayMatrices[1][i][0] = 0;
            this.coefsArrayMatrices[1][i][1] = 0;
            this.coefsArrayMatrices[1][i][2] = 0;
            this.coefsArrayMatrices[1][i][3] = -sourcePoints[i][0];
            this.coefsArrayMatrices[1][i][4] = -sourcePoints[i][1];
            this.coefsArrayMatrices[1][i][5] = -1;
            this.coefsArrayMatrices[1][i][6] =
                destinationPoints[i][1] * sourcePoints[i][0];
            this.coefsArrayMatrices[1][i][7] =
                destinationPoints[i][1] * sourcePoints[i][1];
            this.coefsArrayMatrices[1][i][8] = destinationPoints[i][1];
        }
    }
    solve() {
        this.weightsArrays = solveJointlySvd(this.coefsArrayMatrices, this.pointCount);
    }
    evaluateFunction(newSourcePoint) {
        if (!this.weightsArrays) {
            this.solve();
        }
        if (!this.weightsArrays) {
            throw new Error('Weights not computed');
        }
        const c = this.weightsArrays[0][2] * newSourcePoint[0] +
            this.weightsArrays[1][2] * newSourcePoint[1] +
            this.weightsArrays[2][2];
        const num1 = this.weightsArrays[0][0] * newSourcePoint[0] +
            this.weightsArrays[1][0] * newSourcePoint[1] +
            this.weightsArrays[2][0];
        const num2 = this.weightsArrays[0][1] * newSourcePoint[0] +
            this.weightsArrays[1][1] * newSourcePoint[1] +
            this.weightsArrays[2][1];
        const newDestinationPoint = [num1 / c, num2 / c];
        return newDestinationPoint;
    }
    evaluatePartialDerivativeX(newSourcePoint) {
        if (!this.weightsArrays) {
            this.solve();
        }
        if (!this.weightsArrays) {
            throw new Error('Weights not computed');
        }
        const c = this.weightsArrays[0][2] * newSourcePoint[0] +
            this.weightsArrays[1][2] * newSourcePoint[1] +
            this.weightsArrays[2][2];
        const num1 = this.weightsArrays[0][0] * newSourcePoint[0] +
            this.weightsArrays[1][0] * newSourcePoint[1] +
            this.weightsArrays[2][0];
        const num2 = this.weightsArrays[0][1] * newSourcePoint[0] +
            this.weightsArrays[1][1] * newSourcePoint[1] +
            this.weightsArrays[2][1];
        const newDestinationPointPartDerX = [
            (c * this.weightsArrays[0][0] - this.weightsArrays[0][2] * num1) / c ** 2,
            (c * this.weightsArrays[0][1] - this.weightsArrays[0][2] * num2) / c ** 2
        ];
        return newDestinationPointPartDerX;
    }
    evaluatePartialDerivativeY(newSourcePoint) {
        if (!this.weightsArrays) {
            this.solve();
        }
        if (!this.weightsArrays) {
            throw new Error('Weights not computed');
        }
        const c = this.weightsArrays[0][2] * newSourcePoint[0] +
            this.weightsArrays[1][2] * newSourcePoint[1] +
            this.weightsArrays[2][2];
        const num1 = this.weightsArrays[0][0] * newSourcePoint[0] +
            this.weightsArrays[1][0] * newSourcePoint[1] +
            this.weightsArrays[2][0];
        const num2 = this.weightsArrays[0][1] * newSourcePoint[0] +
            this.weightsArrays[1][1] * newSourcePoint[1] +
            this.weightsArrays[2][1];
        const newDestinationPointPartDerY = [
            (c * this.weightsArrays[1][0] - this.weightsArrays[1][2] * num1) / c ** 2,
            (c * this.weightsArrays[1][1] - this.weightsArrays[1][2] * num2) / c ** 2
        ];
        return newDestinationPointPartDerY;
    }
}