/* This Source Code Form is subject to the terms of the Mozilla Public * License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
"use strict";
/** * Get the distance between two points on a plane. * @param {Number} x1 the x coord of the first point * @param {Number} y1 the y coord of the first point * @param {Number} x2 the x coord of the second point * @param {Number} y2 the y coord of the second point * @returns {Number} the distance between the two points
*/ const getDistance = (x1, y1, x2, y2) => { return Math.round(Math.hypot(x2 - x1, y2 - y1));
};
/** * Determine if the given x/y coords are along the edge of the given ellipse. * We allow for a small area around the edge that still counts as being on the edge. * @param {Number} x the x coordinate of the click * @param {Number} y the y coordinate of the click * @param {Number} cx the x coordinate of the center of the ellipse * @param {Number} cy the y coordinate of the center of the ellipse * @param {Number} rx the x radius of the ellipse * @param {Number} ry the y radius of the ellipse * @param {Number} clickWidthX the width of the area that counts as being on the edge * along the x radius. * @param {Number} clickWidthY the width of the area that counts as being on the edge * along the y radius. * @returns {Boolean} whether the click counts as being on the edge of the ellipse.
*/ const clickedOnEllipseEdge = (
x,
y,
cx,
cy,
rx,
ry,
clickWidthX,
clickWidthY
) => { // The formula to determine if something is inside or on the edge of an ellipse is: // (x - cx)^2/rx^2 + (y - cy)^2/ry^2 <= 1. If > 1, it's outside. // We make two ellipses, adjusting rx and ry with clickWidthX and clickWidthY // to allow for an area around the edge of the ellipse that can be clicked on. // If the click was outside the inner ellipse and inside the outer ellipse, return true. const inner =
(x - cx) ** 2 / (rx - clickWidthX) ** 2 +
(y - cy) ** 2 / (ry - clickWidthY) ** 2; const outer =
(x - cx) ** 2 / (rx + clickWidthX) ** 2 +
(y - cy) ** 2 / (ry + clickWidthY) ** 2; return inner >= 1 && outer <= 1;
};
/** * Get the distance between a point and a line defined by two other points. * @param {Number} x1 the x coordinate of the first point in the line * @param {Number} y1 the y coordinate of the first point in the line * @param {Number} x2 the x coordinate of the second point in the line * @param {Number} y2 the y coordinate of the second point in the line * @param {Number} x3 the x coordinate of the point for which the distance is found * @param {Number} y3 the y coordinate of the point for which the distance is found * @returns {Number} the distance between (x3,y3) and the line defined by * (x1,y1) and (y1,y2)
*/ const distanceToLine = (x1, y1, x2, y2, x3, y3) => { // https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line#Line_defined_by_two_points const num = Math.abs((y2 - y1) * x3 - (x2 - x1) * y3 + x2 * y1 - y2 * x1); const denom = getDistance(x1, y1, x2, y2); return num / denom;
};
/** * Get the point on the line defined by points a,b that is closest to point c * @param {Number} ax the x coordinate of point a * @param {Number} ay the y coordinate of point a * @param {Number} bx the x coordinate of point b * @param {Number} by the y coordinate of point b * @param {Number} cx the x coordinate of point c * @param {Number} cy the y coordinate of point c * @returns {Array} a 2 element array that contains the x/y coords of the projected point
*/ const projection = (ax, ay, bx, by, cx, cy) => { // https://en.wikipedia.org/wiki/Vector_projection#Vector_projection_2 const ab = [bx - ax, by - ay]; const ac = [cx - ax, cy - ay]; const scalar = dotProduct(ab, ac) / dotProduct(ab, ab); return [ax + scalar * ab[0], ay + scalar * ab[1]];
};
/** * Get the dot product of two vectors, represented by arrays of numbers. * @param {Array} a the first vector * @param {Array} b the second vector * @returns {Number} the dot product of a and b
*/ const dotProduct = (a, b) => { return a.reduce((prev, curr, i) => { return prev + curr * b[i];
}, 0);
};
/** * Determine if the given x/y coords are above the given point. * @param {Number} x the x coordinate of the click * @param {Number} y the y coordinate of the click * @param {Number} pointX the x coordinate of the center of the point * @param {Number} pointY the y coordinate of the center of the point * @param {Number} radiusX the x radius of the point * @param {Number} radiusY the y radius of the point * @returns {Boolean} whether the click was on the point
*/ const clickedOnPoint = (x, y, pointX, pointY, radiusX, radiusY) => { return (
x >= pointX - radiusX &&
x <= pointX + radiusX &&
y >= pointY - radiusY &&
y <= pointY + radiusY
);
};
const roundTo = (value, exp) => { // If the exp is undefined or zero... if (typeof exp === "undefined" || +exp === 0) { return Math.round(value);
}
value = +value;
exp = +exp; // If the value is not a number or the exp is not an integer... if (isNaN(value) || !(typeof exp === "number" && exp % 1 === 0)) { return NaN;
} // Shift
value = value.toString().split("e");
value = Math.round(+(value[0] + "e" + (value[1] ? +value[1] - exp : -exp))); // Shift back
value = value.toString().split("e"); return +(value[0] + "e" + (value[1] ? +value[1] + exp : exp));
};
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