🏎️ Simplifies kinematics by removing matrix muls
This commit is contained in:
Rune Harlyk
+112
-307
@@ -1,320 +1,125 @@
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export interface body_state_t {
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omega: number;
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phi: number;
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psi: number;
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xm: number;
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ym: number;
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zm: number;
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feet: number[][];
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omega: number
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phi: number
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psi: number
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xm: number
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ym: number
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zm: number
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feet: number[][]
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}
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export interface position {
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x: number;
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y: number;
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z: number;
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x: number
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y: number
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z: number
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}
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export interface target_position {
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x: number;
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z: number;
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yaw: number;
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x: number
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z: number
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yaw: number
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}
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const { cos, sin, atan2, sqrt } = Math;
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const { cos, sin, atan2, acos, sqrt, max, min } = Math
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const DEG2RAD = 0.017453292519943;
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const DEG2RAD = 0.017453292519943
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export default class Kinematic {
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l1: number;
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l2: number;
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l3: number;
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l4: number;
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L: number;
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W: number;
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DEG2RAD = DEG2RAD;
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sHp = sin(Math.PI / 2);
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cHp = cos(Math.PI / 2);
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Tlf: number[][] = [];
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Trf: number[][] = [];
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Tlb: number[][] = [];
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Trb: number[][] = [];
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point_lf: number[][];
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point_rf: number[][];
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point_lb: number[][];
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point_rb: number[][];
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Ix: number[][];
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constructor() {
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this.l1 = 60.5 / 100;
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this.l2 = 10 / 100;
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this.l3 = 100.7 / 100;
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this.l4 = 118.5 / 100;
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this.L = 207.5 / 100;
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this.W = 78 / 100;
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this.point_lf = [
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[this.cHp, 0, this.sHp, this.L / 2],
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[0, 1, 0, 0],
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[-this.sHp, 0, this.cHp, this.W / 2],
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[0, 0, 0, 1]
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];
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this.point_rf = [
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[this.cHp, 0, this.sHp, this.L / 2],
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[0, 1, 0, 0],
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[-this.sHp, 0, this.cHp, -this.W / 2],
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[0, 0, 0, 1]
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];
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this.point_lb = [
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[this.cHp, 0, this.sHp, -this.L / 2],
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[0, 1, 0, 0],
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[-this.sHp, 0, this.cHp, this.W / 2],
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[0, 0, 0, 1]
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];
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this.point_rb = [
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[this.cHp, 0, this.sHp, -this.L / 2],
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[0, 1, 0, 0],
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[-this.sHp, 0, this.cHp, -this.W / 2],
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[0, 0, 0, 1]
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];
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this.Ix = [
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[-1, 0, 0, 0],
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[0, 1, 0, 0],
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[0, 0, 1, 0],
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[0, 0, 0, 1]
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];
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}
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public calcIK(body_state: body_state_t): number[] {
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this.bodyIK(body_state);
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return [
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...this.legIK(this.multiplyVector(this.inverse(this.Tlf), body_state.feet[0])),
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...this.legIK(
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this.multiplyVector(
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this.Ix,
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this.multiplyVector(this.inverse(this.Trf), body_state.feet[1])
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)
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),
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...this.legIK(this.multiplyVector(this.inverse(this.Tlb), body_state.feet[2])),
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...this.legIK(
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this.multiplyVector(
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this.Ix,
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this.multiplyVector(this.inverse(this.Trb), body_state.feet[3])
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)
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)
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];
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}
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bodyIK(p: body_state_t) {
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const cos_omega = cos(p.omega * this.DEG2RAD);
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const sin_omega = sin(p.omega * this.DEG2RAD);
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const cos_phi = cos(p.phi * this.DEG2RAD);
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const sin_phi = sin(p.phi * this.DEG2RAD);
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const cos_psi = cos(p.psi * this.DEG2RAD);
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const sin_psi = sin(p.psi * this.DEG2RAD);
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const Tm: number[][] = [
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[cos_phi * cos_psi, -sin_psi * cos_phi, sin_phi, p.xm],
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[
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sin_omega * sin_phi * cos_psi + sin_psi * cos_omega,
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-sin_omega * sin_phi * sin_psi + cos_omega * cos_psi,
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-sin_omega * cos_phi,
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p.ym
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],
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[
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sin_omega * sin_psi - sin_phi * cos_omega * cos_psi,
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sin_omega * cos_psi + sin_phi * sin_psi * cos_omega,
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cos_omega * cos_phi,
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p.zm
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],
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[0, 0, 0, 1]
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];
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this.Tlf = this.matrixMultiply(Tm, this.point_lf);
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this.Trf = this.matrixMultiply(Tm, this.point_rf);
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this.Tlb = this.matrixMultiply(Tm, this.point_lb);
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this.Trb = this.matrixMultiply(Tm, this.point_rb);
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}
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public legIK(point: number[]): number[] {
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const [x, y, z] = point;
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let F = sqrt(x ** 2 + y ** 2 - this.l1 ** 2);
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if (isNaN(F)) F = this.l1;
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const G = F - this.l2;
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const H = sqrt(G ** 2 + z ** 2);
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const theta1 = -atan2(y, x) - atan2(F, -this.l1);
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const D = (H ** 2 - this.l3 ** 2 - this.l4 ** 2) / (2 * this.l3 * this.l4);
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let theta3 = atan2(sqrt(1 - D ** 2), D);
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if (isNaN(theta3)) theta3 = 0;
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const theta2 = atan2(z, G) - atan2(this.l4 * sin(theta3), this.l3 + this.l4 * cos(theta3));
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return [theta1, theta2, theta3];
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}
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matrixMultiply(a: number[][], b: number[][]): number[][] {
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const result: number[][] = [];
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for (let i = 0; i < a.length; i++) {
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const row: number[] = [];
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for (let j = 0; j < b[0].length; j++) {
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let sum = 0;
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for (let k = 0; k < a[i].length; k++) {
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sum += a[i][k] * b[k][j];
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}
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row.push(sum);
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}
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result.push(row);
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}
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return result;
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}
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multiplyVector(matrix: number[][], vector: number[]): number[] {
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const rows = matrix.length;
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const cols = matrix[0].length;
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const vectorLength = vector.length;
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if (cols !== vectorLength) {
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throw new Error('Matrix and vector dimensions do not match for multiplication.');
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}
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const result = [];
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for (let i = 0; i < rows; i++) {
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let sum = 0;
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for (let j = 0; j < cols; j++) {
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sum += matrix[i][j] * vector[j];
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}
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result.push(sum);
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}
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return result;
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}
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private inverse(matrix: number[][]): number[][] {
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const det = this.determinant(matrix);
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const adjugate = this.adjugate(matrix);
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const scalar = 1 / det;
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const inverse: number[][] = [];
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for (let i = 0; i < matrix.length; i++) {
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const row: number[] = [];
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for (let j = 0; j < matrix[i].length; j++) {
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row.push(adjugate[i][j] * scalar);
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}
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inverse.push(row);
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}
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return inverse;
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}
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private determinant(matrix: number[][]): number {
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if (matrix.length !== matrix[0].length) {
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throw new Error('The matrix is not square.');
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}
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if (matrix.length === 2) {
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return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
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}
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let det = 0;
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for (let i = 0; i < matrix.length; i++) {
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const sign = i % 2 === 0 ? 1 : -1;
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const subMatrix: number[][] = [];
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for (let j = 1; j < matrix.length; j++) {
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const row: number[] = [];
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for (let k = 0; k < matrix.length; k++) {
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if (k !== i) {
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row.push(matrix[j][k]);
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}
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}
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subMatrix.push(row);
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}
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det += sign * matrix[0][i] * this.determinant(subMatrix);
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}
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return det;
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}
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private adjugate(matrix: number[][]): number[][] {
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if (matrix.length !== matrix[0].length) {
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throw new Error('The matrix is not square.');
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}
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const adjugate: number[][] = [];
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for (let i = 0; i < matrix.length; i++) {
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const row: number[] = [];
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for (let j = 0; j < matrix[i].length; j++) {
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const sign = (i + j) % 2 === 0 ? 1 : -1;
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const subMatrix: number[][] = [];
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for (let k = 0; k < matrix.length; k++) {
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if (k !== i) {
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const subRow: number[] = [];
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for (let l = 0; l < matrix.length; l++) {
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if (l !== j) {
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subRow.push(matrix[k][l]);
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}
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}
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subMatrix.push(subRow);
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}
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}
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const cofactor = sign * this.determinant(subMatrix);
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row.push(cofactor);
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}
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adjugate.push(row);
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}
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return this.transpose(adjugate);
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}
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private transpose(matrix: number[][]): number[][] {
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const transposed: number[][] = [];
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for (let i = 0; i < matrix.length; i++) {
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const row: number[] = [];
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for (let j = 0; j < matrix[i].length; j++) {
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row.push(matrix[j][i]);
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}
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transposed.push(row);
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}
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return transposed;
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}
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l1: number
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l2: number
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l3: number
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l4: number
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L: number
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W: number
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DEG2RAD = DEG2RAD
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mountOffsets: number[][]
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invMountRot = [
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[0, 0, -1],
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[0, 1, 0],
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[1, 0, 0]
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]
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constructor() {
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this.l1 = 60.5 / 100
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this.l2 = 10 / 100
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this.l3 = 100.7 / 100
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this.l4 = 118.5 / 100
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this.L = 230 / 100
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this.W = 75 / 100
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this.mountOffsets = [
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[this.L / 2, 0, this.W / 2],
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[this.L / 2, 0, -this.W / 2],
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[-this.L / 2, 0, this.W / 2],
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[-this.L / 2, 0, -this.W / 2]
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]
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}
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calcIK(p: body_state_t): number[] {
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const roll = p.omega * this.DEG2RAD
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const pitch = p.phi * this.DEG2RAD
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const yaw = p.psi * this.DEG2RAD
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const rot = this.euler2R(roll, pitch, yaw)
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const inv_rot = [
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[rot[0][0], rot[1][0], rot[2][0]],
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[rot[0][1], rot[1][1], rot[2][1]],
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[rot[0][2], rot[1][2], rot[2][2]]
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]
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const inv_trans = [
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-inv_rot[0][0] * p.xm - inv_rot[0][1] * p.ym - inv_rot[0][2] * p.zm,
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-inv_rot[1][0] * p.xm - inv_rot[1][1] * p.ym - inv_rot[1][2] * p.zm,
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-inv_rot[2][0] * p.xm - inv_rot[2][1] * p.ym - inv_rot[2][2] * p.zm
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]
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return p.feet.flatMap((foot, i) => {
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const [wx, wy, wz] = foot
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const bx = inv_rot[0][0] * wx + inv_rot[0][1] * wy + inv_rot[0][2] * wz + inv_trans[0]
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const by = inv_rot[1][0] * wx + inv_rot[1][1] * wy + inv_rot[1][2] * wz + inv_trans[1]
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const bz = inv_rot[2][0] * wx + inv_rot[2][1] * wy + inv_rot[2][2] * wz + inv_trans[2]
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const [mx, my, mz] = this.mountOffsets[i]
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const px = bx - mx,
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py = by - my,
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pz = bz - mz
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const lx =
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this.invMountRot[0][0] * px + this.invMountRot[0][1] * py + this.invMountRot[0][2] * pz
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const ly =
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this.invMountRot[1][0] * px + this.invMountRot[1][1] * py + this.invMountRot[1][2] * pz
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const lz =
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this.invMountRot[2][0] * px + this.invMountRot[2][1] * py + this.invMountRot[2][2] * pz
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const xLocal = i % 2 === 1 ? -lx : lx
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return this.legIK(xLocal, ly, lz)
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})
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}
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private legIK(x: number, y: number, z: number): [number, number, number] {
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const F = sqrt(max(0, x * x + y * y - this.l1 * this.l1))
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const G = F - this.l2
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const H = sqrt(G * G + z * z)
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const t1 = -atan2(y, x) - atan2(F, -this.l1)
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const D = (H * H - this.l3 * this.l3 - this.l4 * this.l4) / (2 * this.l3 * this.l4)
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const t3 = acos(max(-1, min(1, D)))
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const t2 = atan2(z, G) - atan2(this.l4 * sin(t3), this.l3 + this.l4 * cos(t3))
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return [t1, t2, t3]
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}
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private euler2R(roll: number, pitch: number, yaw: number): number[][] {
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const cr = cos(roll),
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sr = sin(roll)
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const cp = cos(pitch),
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sp = sin(pitch)
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const cy = cos(yaw),
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sy = sin(yaw)
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return [
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[cp * cy, -cp * sy, sp],
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[sr * sp * cy + sy * cr, -sr * sp * sy + cr * cy, -sr * cp],
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[sr * sy - sp * cr * cy, sr * cy + sp * sy * cr, cr * cp]
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]
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}
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}
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@@ -3,7 +3,7 @@
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#include <utils/math_utils.h>
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struct body_state_t {
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struct alignas(16) body_state_t {
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float omega, phi, psi, xm, ym, zm;
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float feet[4][4];
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@@ -15,7 +15,7 @@ struct body_state_t {
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!IS_ALMOST_EQUAL(zm, other.zm)) {
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return false;
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}
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return arrayEqual(feet, other.feet, 0.1);
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return arrayEqual(feet, other.feet, 0.1f);
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}
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};
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@@ -23,25 +23,20 @@ class Kinematics {
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private:
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static constexpr float l1 = 60.5f / 100.0f;
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static constexpr float l2 = 10.0f / 100.0f;
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static constexpr float l3 = 111.1f / 100.0f;
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static constexpr float l3 = 111.2f / 100.0f;
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static constexpr float l4 = 118.5f / 100.0f;
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static constexpr float L = 207.5f / 100.0f;
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static constexpr float W = 78.0f / 100.0f;
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const float sHp = sinf(PI_F / 2);
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const float cHp = cosf(PI_F / 2);
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static constexpr float mountOffsets[4][3] = {
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{L / 2, 0, W / 2}, {L / 2, 0, -W / 2}, {-L / 2, 0, W / 2}, {-L / 2, 0, -W / 2}};
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static constexpr float Ix[4][4] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}};
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static constexpr float invMountRot[3][3] = {{0, 0, -1}, {0, 1, 0}, {1, 0, 0}};
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float Trb[4][4] = {0};
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float Trf[4][4] = {0};
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float Tlb[4][4] = {0};
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float Tlf[4][4] = {0};
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float inv[4][4];
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float point[4];
|
||||
float Q1[4][4];
|
||||
alignas(16) float rot[3][3] = {0};
|
||||
alignas(16) float inv_rot[3][3] = {0};
|
||||
alignas(16) float inv_trans[3] = {0};
|
||||
|
||||
body_state_t currentState;
|
||||
|
||||
@@ -51,7 +46,6 @@ class Kinematics {
|
||||
|
||||
if (currentState == body_state) return ESP_OK;
|
||||
|
||||
ret = bodyIK(body_state);
|
||||
currentState.omega = body_state.omega;
|
||||
currentState.phi = body_state.phi;
|
||||
currentState.psi = body_state.psi;
|
||||
@@ -60,100 +54,91 @@ class Kinematics {
|
||||
currentState.zm = body_state.zm;
|
||||
currentState.updateFeet(body_state.feet);
|
||||
|
||||
ret += inverse(Tlf, inv);
|
||||
MAT_MULT(inv, body_state.feet[0], point, 4, 4, 1);
|
||||
legIK((float *)point, result);
|
||||
float roll = body_state.omega * DEG2RAD_F;
|
||||
float pitch = body_state.phi * DEG2RAD_F;
|
||||
float yaw = body_state.psi * DEG2RAD_F;
|
||||
euler2R(roll, pitch, yaw, rot);
|
||||
inverse(rot, inv_rot);
|
||||
|
||||
ret += inverse(Trf, inv);
|
||||
MAT_MULT(Ix, inv, Q1, 4, 4, 4);
|
||||
MAT_MULT(Q1, body_state.feet[1], point, 4, 4, 1);
|
||||
legIK((float *)point, result + 3);
|
||||
inv_trans[0] =
|
||||
-inv_rot[0][0] * currentState.xm - inv_rot[0][1] * currentState.ym - inv_rot[0][2] * currentState.zm;
|
||||
inv_trans[1] =
|
||||
-inv_rot[1][0] * currentState.xm - inv_rot[1][1] * currentState.ym - inv_rot[1][2] * currentState.zm;
|
||||
inv_trans[2] =
|
||||
-inv_rot[2][0] * currentState.xm - inv_rot[2][1] * currentState.ym - inv_rot[2][2] * currentState.zm;
|
||||
|
||||
ret += inverse(Tlb, inv);
|
||||
MAT_MULT(inv, body_state.feet[2], point, 4, 4, 1);
|
||||
legIK((float *)point, result + 6);
|
||||
for (int i = 0; i < 4; i++) {
|
||||
float wx = currentState.feet[i][0];
|
||||
float wy = currentState.feet[i][1];
|
||||
float wz = currentState.feet[i][2];
|
||||
|
||||
ret += inverse(Trb, inv);
|
||||
MAT_MULT(Ix, inv, Q1, 4, 4, 4);
|
||||
MAT_MULT(Q1, body_state.feet[3], point, 4, 4, 1);
|
||||
legIK((float *)point, result + 9);
|
||||
float bx = inv_rot[0][0] * wx + inv_rot[0][1] * wy + inv_rot[0][2] * wz + inv_trans[0];
|
||||
float by = inv_rot[1][0] * wx + inv_rot[1][1] * wy + inv_rot[1][2] * wz + inv_trans[1];
|
||||
float bz = inv_rot[2][0] * wx + inv_rot[2][1] * wy + inv_rot[2][2] * wz + inv_trans[2];
|
||||
|
||||
float mx = mountOffsets[i][0];
|
||||
float my = mountOffsets[i][1];
|
||||
float mz = mountOffsets[i][2];
|
||||
|
||||
float px = bx - mx;
|
||||
float py = by - my;
|
||||
float pz = bz - mz;
|
||||
|
||||
float lx = invMountRot[0][0] * px + invMountRot[0][1] * py + invMountRot[0][2] * pz;
|
||||
float ly = invMountRot[1][0] * px + invMountRot[1][1] * py + invMountRot[1][2] * pz;
|
||||
float lz = invMountRot[2][0] * px + invMountRot[2][1] * py + invMountRot[2][2] * pz;
|
||||
|
||||
float xLocal = (i % 2 == 1) ? -lx : lx;
|
||||
legIK(xLocal, ly, lz, result + i * 3);
|
||||
}
|
||||
|
||||
return ret;
|
||||
}
|
||||
|
||||
esp_err_t bodyIK(const body_state_t p) {
|
||||
float cos_omega = COS_DEG_F(p.omega);
|
||||
float sin_omega = SIN_DEG_F(p.omega);
|
||||
float cos_phi = COS_DEG_F(p.phi);
|
||||
float sin_phi = SIN_DEG_F(p.phi);
|
||||
float cos_psi = COS_DEG_F(p.psi);
|
||||
float sin_psi = SIN_DEG_F(p.psi);
|
||||
inline void euler2R(float roll, float pitch, float yaw, float rot[3][3]) {
|
||||
float cos_roll = std::cos(roll);
|
||||
float sin_roll = std::sin(roll);
|
||||
float cos_pitch = std::cos(pitch);
|
||||
float sin_pitch = std::sin(pitch);
|
||||
float cos_yaw = std::cos(yaw);
|
||||
float sin_yaw = std::sin(yaw);
|
||||
|
||||
float Tm[4][4] = {{cos_phi * cos_psi, -sin_psi * cos_phi, sin_phi, p.xm},
|
||||
{sin_omega * sin_phi * cos_psi + sin_psi * cos_omega,
|
||||
-sin_omega * sin_phi * sin_psi + cos_omega * cos_psi, -sin_omega * cos_phi, p.ym},
|
||||
{sin_omega * sin_psi - sin_phi * cos_omega * cos_psi,
|
||||
sin_omega * cos_psi + sin_phi * sin_psi * cos_omega, cos_omega * cos_phi, p.zm},
|
||||
{0, 0, 0, 1}};
|
||||
|
||||
float point_lf[4][4] = {{cHp, 0, sHp, L / 2}, {0, 1, 0, 0}, {-sHp, 0, cHp, W / 2}, {0, 0, 0, 1}};
|
||||
float point_rf[4][4] = {{cHp, 0, sHp, L / 2}, {0, 1, 0, 0}, {-sHp, 0, cHp, -W / 2}, {0, 0, 0, 1}};
|
||||
float point_lb[4][4] = {{cHp, 0, sHp, -L / 2}, {0, 1, 0, 0}, {-sHp, 0, cHp, W / 2}, {0, 0, 0, 1}};
|
||||
float point_rb[4][4] = {{cHp, 0, sHp, -L / 2}, {0, 1, 0, 0}, {-sHp, 0, cHp, -W / 2}, {0, 0, 0, 1}};
|
||||
|
||||
MAT_MULT(Tm, point_lf, Tlf, 4, 4, 4);
|
||||
MAT_MULT(Tm, point_rf, Trf, 4, 4, 4);
|
||||
MAT_MULT(Tm, point_lb, Tlb, 4, 4, 4);
|
||||
MAT_MULT(Tm, point_rb, Trb, 4, 4, 4);
|
||||
return ESP_OK;
|
||||
rot[0][0] = cos_pitch * cos_yaw;
|
||||
rot[0][1] = -sin_yaw * cos_pitch;
|
||||
rot[0][2] = sin_pitch;
|
||||
rot[1][0] = sin_roll * sin_pitch * cos_yaw + sin_yaw * cos_roll;
|
||||
rot[1][1] = -sin_roll * sin_pitch * sin_yaw + cos_roll * cos_yaw;
|
||||
rot[1][2] = -sin_roll * cos_pitch;
|
||||
rot[2][0] = sin_roll * sin_yaw - sin_pitch * cos_roll * cos_yaw;
|
||||
rot[2][1] = sin_roll * cos_yaw + sin_pitch * sin_yaw * cos_roll;
|
||||
rot[2][2] = cos_roll * cos_pitch;
|
||||
}
|
||||
|
||||
void legIK(float point[4], float result[3]) {
|
||||
float x = point[0], y = point[1], z = point[2];
|
||||
inline void inverse(float rot[3][3], float inv_rot[3][3]) {
|
||||
inv_rot[0][0] = rot[0][0];
|
||||
inv_rot[0][1] = rot[1][0];
|
||||
inv_rot[0][2] = rot[2][0];
|
||||
inv_rot[1][0] = rot[0][1];
|
||||
inv_rot[1][1] = rot[1][1];
|
||||
inv_rot[1][2] = rot[2][1];
|
||||
inv_rot[2][0] = rot[0][2];
|
||||
inv_rot[2][1] = rot[1][2];
|
||||
inv_rot[2][2] = rot[2][2];
|
||||
}
|
||||
|
||||
float F = sqrtf(x * x + y * y - l1 * l1);
|
||||
F = isnanf(F) ? l1 : F;
|
||||
inline void legIK(float x, float y, float z, float result[3]) {
|
||||
float F = sqrt(max(0.0f, x * x + y * y - l1 * l1));
|
||||
float G = F - l2;
|
||||
float H = sqrtf(G * G + z * z);
|
||||
float H = sqrt(G * G + z * z);
|
||||
|
||||
float theta1 = -atan2f(y, x) - atan2f(F, -l1);
|
||||
float D = (H * H - l3 * l3 - l4 * l4) / (2 * l3 * l4);
|
||||
float theta3 = atan2(sqrt(1 - D * D), D);
|
||||
if (isnan(theta3)) theta3 = 0;
|
||||
float theta3 = acosf(max(-1.0f, min(1.0f, D)));
|
||||
float theta2 = atan2f(z, G) - atan2f(l4 * sinf(theta3), l3 + l4 * cosf(theta3));
|
||||
result[0] = RAD_TO_DEG_F(theta1);
|
||||
result[1] = RAD_TO_DEG_F(theta2);
|
||||
result[2] = RAD_TO_DEG_F(theta3);
|
||||
}
|
||||
|
||||
esp_err_t inverse(float a[4][4], float b[4][4]) {
|
||||
float s[] = {a[0][0] * a[1][1] - a[1][0] * a[0][1], a[0][0] * a[1][2] - a[1][0] * a[0][2],
|
||||
a[0][0] * a[1][3] - a[1][0] * a[0][3], a[0][1] * a[1][2] - a[1][1] * a[0][2],
|
||||
a[0][1] * a[1][3] - a[1][1] * a[0][3], a[0][2] * a[1][3] - a[1][2] * a[0][3]};
|
||||
float c[] = {a[2][0] * a[3][1] - a[3][0] * a[2][1], a[2][0] * a[3][2] - a[3][0] * a[2][2],
|
||||
a[2][0] * a[3][3] - a[3][0] * a[2][3], a[2][1] * a[3][2] - a[3][1] * a[2][2],
|
||||
a[2][1] * a[3][3] - a[3][1] * a[2][3], a[2][2] * a[3][3] - a[3][2] * a[2][3]};
|
||||
float det = s[0] * c[5] - s[1] * c[4] + s[2] * c[3] + s[3] * c[2] - s[4] * c[1] + s[5] * c[0];
|
||||
if (det == 0.0) return ESP_FAIL;
|
||||
float invdet = 1.0 / det;
|
||||
b[0][0] = (a[1][1] * c[5] - a[1][2] * c[4] + a[1][3] * c[3]) * invdet;
|
||||
b[0][1] = (-a[0][1] * c[5] + a[0][2] * c[4] - a[0][3] * c[3]) * invdet;
|
||||
b[0][2] = (a[3][1] * s[5] - a[3][2] * s[4] + a[3][3] * s[3]) * invdet;
|
||||
b[0][3] = (-a[2][1] * s[5] + a[2][2] * s[4] - a[2][3] * s[3]) * invdet;
|
||||
b[1][0] = (-a[1][0] * c[5] + a[1][2] * c[2] - a[1][3] * c[1]) * invdet;
|
||||
b[1][1] = (a[0][0] * c[5] - a[0][2] * c[2] + a[0][3] * c[1]) * invdet;
|
||||
b[1][2] = (-a[3][0] * s[5] + a[3][2] * s[2] - a[3][3] * s[1]) * invdet;
|
||||
b[1][3] = (a[2][0] * s[5] - a[2][2] * s[2] + a[2][3] * s[1]) * invdet;
|
||||
b[2][0] = (a[1][0] * c[4] - a[1][1] * c[2] + a[1][3] * c[0]) * invdet;
|
||||
b[2][1] = (-a[0][0] * c[4] + a[0][1] * c[2] - a[0][3] * c[0]) * invdet;
|
||||
b[2][2] = (a[3][0] * s[4] - a[3][1] * s[2] + a[3][3] * s[0]) * invdet;
|
||||
b[2][3] = (-a[2][0] * s[4] + a[2][1] * s[2] - a[2][3] * s[0]) * invdet;
|
||||
b[3][0] = (-a[1][0] * c[3] + a[1][1] * c[1] - a[1][2] * c[0]) * invdet;
|
||||
b[3][1] = (a[0][0] * c[3] - a[0][1] * c[1] + a[0][2] * c[0]) * invdet;
|
||||
b[3][2] = (-a[3][0] * s[3] + a[3][1] * s[1] - a[3][2] * s[0]) * invdet;
|
||||
b[3][3] = (a[2][0] * s[3] - a[2][1] * s[1] + a[2][2] * s[0]) * invdet;
|
||||
return ESP_OK;
|
||||
}
|
||||
};
|
||||
|
||||
#endif
|
||||
Reference in New Issue
Block a user