/*
* Copyright 2024 The Ray Optics Simulation authors and contributors
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
import BaseFilter from '../BaseFilter.js';
import i18next from 'i18next';
import Simulator from '../../Simulator.js';
import geometry from '../../geometry.js';
/**
* Parabolic mirror.
*
* Tools -> Mirror -> Parabolic
*
* The current implementation is based on `CustomMirror.js`, but this should be changed to an analytical solution in the future.
* @class
* @extends BaseFilter
* @memberof sceneObjs
* @property {Point} p1 - The first endpoint.
* @property {Point} p2 - The second endpoint.
* @property {Point} p3 - The vertex.
* @property {boolean} filter - Whether it is a dichroic mirror.
* @property {boolean} invert - If true, the ray with wavelength outside the bandwidth is reflected. If false, the ray with wavelength inside the bandwidth is reflected.
* @property {number} wavelength - The target wavelength if dichroic is enabled. The unit is nm.
* @property {number} bandwidth - The bandwidth if dichroic is enabled. The unit is nm.
* @property {Array<Point>} tmp_points - The points on the parabola.
* @property {number} tmp_i - The index of the point on the parabola where the ray is incident.
*/
class ParabolicMirror extends BaseFilter {
static type = 'ParabolicMirror';
static isOptical = true;
static serializableDefaults = {
p1: null,
p2: null,
p3: null,
filter: false,
invert: false,
wavelength: Simulator.GREEN_WAVELENGTH,
bandwidth: 10
};
populateObjBar(objBar) {
objBar.setTitle(i18next.t('main:meta.parentheses', { main: i18next.t('main:tools.categories.mirror'), sub: i18next.t('main:tools.ParabolicMirror.title') }));
super.populateObjBar(objBar);
}
draw(canvasRenderer, isAboveLight, isHovered) {
const ctx = canvasRenderer.ctx;
const ls = canvasRenderer.lengthScale;
ctx.fillStyle = 'rgb(255,0,255)';
if (this.p3 && this.p2) {
var p12d = geometry.distance(this.p1, this.p2);
// unit vector from p1 to p2
var dir1 = [(this.p2.x - this.p1.x) / p12d, (this.p2.y - this.p1.y) / p12d];
// perpendicular direction
var dir2 = [dir1[1], -dir1[0]];
// get height of (this section of) parabola
var height = (this.p3.x - this.p1.x) * dir2[0] + (this.p3.y - this.p1.y) * dir2[1];
// reposition p3 to be at vertex
this.p3 = geometry.point((this.p1.x + this.p2.x) * .5 + dir2[0] * height, (this.p1.y + this.p2.y) * .5 + dir2[1] * height);
var x0 = p12d / 2;
var a = height / (x0 * x0); // y=ax^2
var i;
ctx.strokeStyle = isHovered ? 'cyan' : ((this.scene.simulateColors && this.wavelength && this.filter) ? canvasRenderer.rgbaToCssColor(Simulator.wavelengthToColor(this.wavelength || Simulator.GREEN_WAVELENGTH, 1)) : 'rgb(168,168,168)');
ctx.lineWidth = 1 * ls;
ctx.beginPath();
this.tmp_points = [geometry.point(this.p1.x, this.p1.y)];
ctx.moveTo(this.p1.x, this.p1.y);
for (i = 0.1 * this.scene.lengthScale; i < p12d; i += 0.1 * this.scene.lengthScale) {
// avoid using exact integers to avoid problems with detecting intersections
var ix = i + .001 * this.scene.lengthScale;
var x = ix - x0;
var y = height - a * x * x;
var pt = geometry.point(this.p1.x + dir1[0] * ix + dir2[0] * y, this.p1.y + dir1[1] * ix + dir2[1] * y);
ctx.lineTo(pt.x, pt.y);
this.tmp_points.push(pt);
}
ctx.stroke();
if (isHovered) {
ctx.fillRect(this.p3.x - 1.5 * ls, this.p3.y - 1.5 * ls, 3 * ls, 3 * ls);
var focusx = (this.p1.x + this.p2.x) * .5 + dir2[0] * (height - 1 / (4 * a));
var focusy = (this.p1.y + this.p2.y) * .5 + dir2[1] * (height - 1 / (4 * a));
ctx.fillRect(focusx - 1.5 * ls, focusy - 1.5 * ls, 3 * ls, 3 * ls);
ctx.fillStyle = 'rgb(255,0,0)';
ctx.fillRect(this.p1.x - 1.5 * ls, this.p1.y - 1.5 * ls, 3 * ls, 3 * ls);
ctx.fillRect(this.p2.x - 1.5 * ls, this.p2.y - 1.5 * ls, 3 * ls, 3 * ls);
}
} else if (this.p2) {
ctx.fillStyle = 'rgb(255,0,0)';
ctx.fillRect(this.p1.x - 1.5 * ls, this.p1.y - 1.5 * ls, 3 * ls, 3 * ls);
ctx.fillRect(this.p2.x - 1.5 * ls, this.p2.y - 1.5 * ls, 3 * ls, 3 * ls);
} else {
ctx.fillStyle = 'rgb(255,0,0)';
ctx.fillRect(this.p1.x - 1.5 * ls, this.p1.y - 1.5 * ls, 3 * ls, 3 * ls);
}
}
move(diffX, diffY) {
this.p1.x = this.p1.x + diffX;
this.p1.y = this.p1.y + diffY;
this.p2.x = this.p2.x + diffX;
this.p2.y = this.p2.y + diffY;
this.p3.x = this.p3.x + diffX;
this.p3.y = this.p3.y + diffY;
}
onConstructMouseDown(mouse, ctrl, shift) {
if (!this.constructionPoint) {
// Initialize the construction stage.
this.constructionPoint = mouse.getPosSnappedToGrid();
this.p1 = this.constructionPoint;
this.p2 = null;
this.p3 = null;
}
if (!this.p2 && !this.p3) {
this.p2 = mouse.getPosSnappedToGrid();
return;
}
if (this.p2 && !this.p3 && !mouse.snapsOnPoint(this.p1)) {
if (shift) {
this.p2 = mouse.getPosSnappedToDirection(this.p1, [{ x: 1, y: 0 }, { x: 0, y: 1 }, { x: 1, y: 1 }, { x: 1, y: -1 }]);
} else {
this.p2 = mouse.getPosSnappedToGrid();
}
this.p3 = mouse.getPosSnappedToGrid();
return;
}
}
onConstructMouseMove(mouse, ctrl, shift) {
if (!this.p3 && !mouse.isOnPoint(this.p1)) {
if (shift) {
this.p2 = mouse.getPosSnappedToDirection(this.constructionPoint, [{ x: 1, y: 0 }, { x: 0, y: 1 }, { x: 1, y: 1 }, { x: 1, y: -1 }]);
} else {
this.p2 = mouse.getPosSnappedToGrid();
}
this.p1 = ctrl ? geometry.point(2 * this.constructionPoint.x - this.p2.x, 2 * this.constructionPoint.y - this.p2.y) : this.constructionPoint;
return;
}
if (this.p3) {
this.p3 = mouse.getPosSnappedToGrid();
return;
}
}
onConstructMouseUp(mouse, ctrl, shift) {
if (this.p2 && !this.p3 && !mouse.isOnPoint(this.p1)) {
this.p3 = mouse.getPosSnappedToGrid();
return;
}
if (this.p3 && !mouse.isOnPoint(this.p2)) {
this.p3 = mouse.getPosSnappedToGrid();
delete this.constructionPoint;
return {
isDone: true
};
}
}
checkMouseOver(mouse) {
let dragContext = {};
if (mouse.isOnPoint(this.p1) && geometry.distanceSquared(mouse.pos, this.p1) <= geometry.distanceSquared(mouse.pos, this.p2) && geometry.distanceSquared(mouse.pos, this.p1) <= geometry.distanceSquared(mouse.pos, this.p3)) {
dragContext.part = 1;
dragContext.targetPoint = geometry.point(this.p1.x, this.p1.y);
return dragContext;
}
if (this.p2 && mouse.isOnPoint(this.p2) && geometry.distanceSquared(mouse.pos, this.p2) <= geometry.distanceSquared(mouse.pos, this.p3)) {
dragContext.part = 2;
dragContext.targetPoint = geometry.point(this.p2.x, this.p2.y);
return dragContext;
}
if (this.p3 && mouse.isOnPoint(this.p3)) {
dragContext.part = 3;
dragContext.targetPoint = geometry.point(this.p3.x, this.p3.y);
return dragContext;
}
if (!this.tmp_points) return;
var i;
var pts = this.tmp_points;
for (i = 0; i < pts.length - 1; i++) {
var seg = geometry.line(pts[i], pts[i + 1]);
if (mouse.isOnSegment(seg)) {
const mousePos = mouse.getPosSnappedToGrid();
dragContext.part = 0;
dragContext.mousePos0 = mousePos;
dragContext.mousePos1 = mousePos;
dragContext.snapContext = {};
return dragContext;
}
}
}
onDrag(mouse, dragContext, ctrl, shift) {
var basePoint;
if (dragContext.part == 1) {
// Dragging the first endpoint
basePoint = ctrl ? geometry.segmentMidpoint(dragContext.originalObj) : dragContext.originalObj.p2;
this.p1 = shift ? mouse.getPosSnappedToDirection(basePoint, [{ x: 1, y: 0 }, { x: 0, y: 1 }, { x: 1, y: 1 }, { x: 1, y: -1 }, { x: (dragContext.originalObj.p2.x - dragContext.originalObj.p1.x), y: (dragContext.originalObj.p2.y - dragContext.originalObj.p1.y) }]) : mouse.getPosSnappedToGrid();
this.p2 = ctrl ? geometry.point(2 * basePoint.x - this.p1.x, 2 * basePoint.y - this.p1.y) : basePoint;
}
if (dragContext.part == 2) {
// Dragging the second endpoint
basePoint = ctrl ? geometry.segmentMidpoint(dragContext.originalObj) : dragContext.originalObj.p1;
this.p2 = shift ? mouse.getPosSnappedToDirection(basePoint, [{ x: 1, y: 0 }, { x: 0, y: 1 }, { x: 1, y: 1 }, { x: 1, y: -1 }, { x: (dragContext.originalObj.p2.x - dragContext.originalObj.p1.x), y: (dragContext.originalObj.p2.y - dragContext.originalObj.p1.y) }]) : mouse.getPosSnappedToGrid();
this.p1 = ctrl ? geometry.point(2 * basePoint.x - this.p2.x, 2 * basePoint.y - this.p2.y) : basePoint;
}
if (dragContext.part == 3) {
// Dragging the third endpoint
this.p3 = mouse.getPosSnappedToGrid();
}
if (dragContext.part == 0) {
// Dragging the entire obj
if (shift) {
var mousePos = mouse.getPosSnappedToDirection(dragContext.mousePos0, [{ x: 1, y: 0 }, { x: 0, y: 1 }, { x: (dragContext.originalObj.p2.x - dragContext.originalObj.p1.x), y: (dragContext.originalObj.p2.y - dragContext.originalObj.p1.y) }, { x: (dragContext.originalObj.p2.y - dragContext.originalObj.p1.y), y: -(dragContext.originalObj.p2.x - dragContext.originalObj.p1.x) }], dragContext.snapContext);
} else {
var mousePos = mouse.getPosSnappedToGrid();;
dragContext.snapContext = {}; // Unlock the dragging direction when the user release the shift key
}
var mouseDiffX = dragContext.mousePos1.x - mousePos.x; // The X difference between the mouse position now and at the previous moment
var mouseDiffY = dragContext.mousePos1.y - mousePos.y; // The Y difference between the mouse position now and at the previous moment
// Move the first point
this.p1.x = this.p1.x - mouseDiffX;
this.p1.y = this.p1.y - mouseDiffY;
// Move the second point
this.p2.x = this.p2.x - mouseDiffX;
this.p2.y = this.p2.y - mouseDiffY;
this.p3.x = this.p3.x - mouseDiffX;
this.p3.y = this.p3.y - mouseDiffY;
// Update the mouse position
dragContext.mousePos1 = mousePos;
}
}
/**
* Transform a point from global coordinates to local parabola coordinates
* where the origin is at p3 (vertex), x-axis along p1-p2,
* and y-axis perpendicular to p1-p2
* @param {Point} point - Point in global coordinates
* @returns {Object} Transformed point {x, y}
*/
transformToLocal(point) {
const p12d = geometry.distance(this.p1, this.p2);
// unit vector from p1 to p2
const dir1 = [(this.p2.x - this.p1.x) / p12d, (this.p2.y - this.p1.y) / p12d];
// perpendicular direction
const dir2 = [dir1[1], -dir1[0]];
// Use p3 as origin instead of midpoint
const dx = point.x - this.p3.x;
const dy = point.y - this.p3.y;
return {
x: dx * dir1[0] + dy * dir1[1],
y: dx * dir2[0] + dy * dir2[1]
};
}
/**
* Transform a point from local parabola coordinates back to global coordinates
* @param {Object} point - Point in local coordinates {x, y}
* @returns {Point} Point in global coordinates
*/
transformToGlobal(point) {
const p12d = geometry.distance(this.p1, this.p2);
// unit vector from p1 to p2
const dir1 = [(this.p2.x - this.p1.x) / p12d, (this.p2.y - this.p1.y) / p12d];
// perpendicular direction
const dir2 = [dir1[1], -dir1[0]];
return geometry.point(
this.p3.x + point.x * dir1[0] + point.y * dir2[0],
this.p3.y + point.x * dir1[1] + point.y * dir2[1]
);
}
/**
* Get the parabola coefficient 'a' in y = ax²
* @returns {number} Coefficient a
*/
getParabolaCoefficient() {
const p12d = geometry.distance(this.p1, this.p2);
const p1Local = this.transformToLocal(this.p1);
// Calculate a from the fact that p1 lies on the parabola
return p1Local.y / (p1Local.x * p1Local.x);
}
/**
* Check if the parabola is degenerate (p1, p2, p3 are collinear)
* @returns {boolean} True if degenerate
*/
isDegenerate() {
// Calculate area of triangle formed by p1, p2, p3
// If area is close to 0, points are collinear
const area = Math.abs(
(this.p2.x - this.p1.x) * (this.p3.y - this.p1.y) -
(this.p3.x - this.p1.x) * (this.p2.y - this.p1.y)
);
return area < 1e-10;
}
checkRayIntersects(ray) {
if (!this.p3 || !this.checkRayIntersectFilter(ray)) return;
// Handle degenerate case (linear mirror)
if (this.isDegenerate()) {
const intersection = geometry.linesIntersection(
geometry.line(ray.p1, ray.p2),
geometry.line(this.p1, this.p2)
);
if (intersection &&
geometry.intersectionIsOnSegment(intersection, geometry.line(this.p1, this.p2)) &&
geometry.intersectionIsOnRay(intersection, ray) &&
geometry.distance(ray.p1, intersection) >= Simulator.MIN_RAY_SEGMENT_LENGTH * this.scene.lengthScale) {
return intersection;
}
return null;
}
// Normal parabolic case
// Transform ray to local coordinates
const p1Local = this.transformToLocal(ray.p1);
const p2Local = this.transformToLocal(ray.p2);
// Get normalized direction vector
const dx = p2Local.x - p1Local.x;
const dy = p2Local.y - p1Local.y;
const d = Math.sqrt(dx * dx + dy * dy);
const vx = dx / d;
const vy = dy / d;
// Get parabola coefficient
const a = this.getParabolaCoefficient();
// Handle the case where ray is parallel to axis of symmetry
// In this case, vx ≈ 0 and the quadratic equation becomes degenerate
if (Math.abs(vx) < 1e-10) {
// For vertical rays, x stays constant
const x = p1Local.x;
// Intersection occurs at y = ax²
const y = a * x * x;
// Calculate time to reach intersection
const t = (y - p1Local.y) / vy;
if (t > Simulator.MIN_RAY_SEGMENT_LENGTH * this.scene.lengthScale &&
Math.abs(x) <= geometry.distance(this.p1, this.p2) / 2) {
return this.transformToGlobal({x, y});
}
return null;
}
// Solve quadratic equation: a·dx²·t² + (2a·x₁·dx - dy)·t + (a·x₁² - y₁) = 0
const A = a * vx * vx;
const B = 2 * a * p1Local.x * vx - vy;
const C = a * p1Local.x * p1Local.x - p1Local.y;
const discriminant = B * B - 4 * A * C;
if (discriminant < 0) return null;
// Use a stable quadratic formula
const sqrtDisc = Math.sqrt(discriminant);
let t1, t2;
if (B > 0) {
t1 = (-B - sqrtDisc) / (2 * A);
} else {
t1 = (-B + sqrtDisc) / (2 * A);
}
t2 = C / (A * t1);
// Get intersection points
const intersections = [];
if (t1 > Simulator.MIN_RAY_SEGMENT_LENGTH * this.scene.lengthScale) {
const x = p1Local.x + t1 * vx;
const y = p1Local.y + t1 * vy;
// Check if point is within the mirror bounds
if (Math.abs(x) <= geometry.distance(this.p1, this.p2) / 2) {
intersections.push({t: t1, point: this.transformToGlobal({x, y})});
}
}
if (t2 > Simulator.MIN_RAY_SEGMENT_LENGTH * this.scene.lengthScale) {
const x = p1Local.x + t2 * vx;
const y = p1Local.y + t2 * vy;
// Check if point is within the mirror bounds
if (Math.abs(x) <= geometry.distance(this.p1, this.p2) / 2) {
intersections.push({t: t2, point: this.transformToGlobal({x, y})});
}
}
// Return closest intersection
if (intersections.length === 0) return null;
return intersections.reduce((closest, current) =>
current.t < closest.t ? current : closest
).point;
}
onRayIncident(ray, rayIndex, incidentPoint) {
// Handle degenerate case (linear mirror)
if (this.isDegenerate()) {
const dir = [(this.p2.x - this.p1.x), (this.p2.y - this.p1.y)];
const len = Math.sqrt(dir[0] * dir[0] + dir[1] * dir[1]);
const nx = -dir[1] / len; // Normal vector
const ny = dir[0] / len;
// Calculate incident vector
const dx = incidentPoint.x - ray.p1.x;
const dy = incidentPoint.y - ray.p1.y;
const d = Math.sqrt(dx * dx + dy * dy);
const vx = dx / d;
const vy = dy / d;
// Calculate reflection using r = v - 2(v·n)n
const dot = vx * nx + vy * ny;
const rx = vx - 2 * dot * nx;
const ry = vy - 2 * dot * ny;
ray.p1 = incidentPoint;
ray.p2 = geometry.point(
incidentPoint.x + rx,
incidentPoint.y + ry
);
return;
}
// Normal parabolic case
// Transform to local coordinates
const incidentLocal = this.transformToLocal(incidentPoint);
const rayStartLocal = this.transformToLocal(ray.p1);
// Get incident direction
const dx = incidentLocal.x - rayStartLocal.x;
const dy = incidentLocal.y - rayStartLocal.y;
const d = Math.sqrt(dx * dx + dy * dy);
const vx = dx / d;
const vy = dy / d;
// Get parabola coefficient
const a = this.getParabolaCoefficient();
// Calculate normal vector at intersection point (-2ax, 1)
const nx = -2 * a * incidentLocal.x;
const ny = 1;
const nlen = Math.sqrt(nx * nx + ny * ny);
const nnx = nx / nlen;
const nny = ny / nlen;
// Calculate reflection direction: r = v - 2(v·n)n
const dot = vx * nnx + vy * nny;
const rx = vx - 2 * dot * nnx;
const ry = vy - 2 * dot * nny;
// Set new ray endpoint in global coordinates
ray.p1 = incidentPoint;
const reflectedPoint = this.transformToGlobal({
x: incidentLocal.x + rx,
y: incidentLocal.y + ry
});
ray.p2 = reflectedPoint;
}
};
export default ParabolicMirror;