desk2/client/math.js

function screen_to_canvas(state, p) {
    // should be called with coordinates obtained from MouseEvent.clientX/clientY * window.devicePixelRatio
    const xc = (p.x - state.canvas.offset.x) / state.canvas.zoom;
    const yc = (p.y - state.canvas.offset.y) / state.canvas.zoom;

    return {'x': xc, 'y': yc};
}

function point_right_of_line(a, b, p) {
    // a bit of cross-product tomfoolery (we check sign of z of the crossproduct)
    return ((b.x - a.x) * (a.y - p.y) - (a.y - b.y) * (p.x - a.x)) <= 0;
}

function rdp_find_max(state, points, start, end) {
    const EPS = 0.5 / state.canvas.zoom;
    // const EPS = 10.0;

    let result = -1;
    let max_dist = 0;

    const a = points[start];
    const b = points[end];

    const dx = b.x - a.x;
    const dy = b.y - a.y;

    const dist_ab = Math.sqrt(dx * dx + dy * dy);
    const sin_theta = dy / dist_ab;
    const cos_theta = dx / dist_ab;

    for (let i = start; i < end; ++i) {
        const p = points[i];
        
        const ox = p.x - a.x;
        const oy = p.y - a.y;

        const rx = cos_theta * ox + sin_theta * oy;
        const ry = -sin_theta * ox + cos_theta * oy;

        const x = rx + a.x;
        const y = ry + a.y;

        const dist = Math.abs(y - a.y);

        if (dist > EPS && dist > max_dist) {
            result = i;
            max_dist = dist;
        }
    }

    return result;
}

function process_rdp_r(state, points, start, end) {
    let result = [];
    
    const max = rdp_find_max(state, points, start, end);

    if (max !== -1) {
        const before = process_rdp_r(state, points, start, max);
        const after = process_rdp_r(state, points, max, end);
        result = [...before, points[max], ...after];
    }

    return result;
}

function process_rdp(state, points) {
    const result = process_rdp_r(state, points, 0, points.length - 1);
    result.unshift(points[0]);
    result.push(points[points.length - 1]);
    return result;
}

function process_ewmv(points, round = false) {
    const result = [];
    const alpha = 0.5;

    result.push(points[0]);

    for (let i = 1; i < points.length; ++i) {
        const p = points[i];
        const x = Math.round(alpha * p.x + (1 - alpha) * result[result.length - 1].x);
        const y = Math.round(alpha * p.y + (1 - alpha) * result[result.length - 1].y);
        result.push({'x': x, 'y': y});
    }

    return result;
}

function process_stroke(state, points) {
    // const result0 = process_ewmv(points);
    const result1 = process_rdp(state, points, true);
    return result1;
}

function stroke_stats(points, width) {
    if (points.length === 0) {
        const bbox = {
            'xmin': 0,
            'ymin': 0,
            'xmax': 0,
            'ymax': 0
        };

        return {
            'bbox': bbox,
            'length': 0,
        };
    }

    let length = 0;
    let xmin = points[0].x, ymin = points[0].y;
    let xmax = xmin, ymax = ymin;

    for (let i = 0; i < points.length; ++i) {
        const point = points[i];
        if (point.x < xmin) xmin = point.x;
        if (point.y < ymin) ymin = point.y;
        if (point.x > xmax) xmax = point.x;
        if (point.y > ymax) ymax = point.y;

        if (i > 0) {
            const last = points[i - 1];
            const dx = point.x - last.x;
            const dy = point.y - last.y;
            length += Math.sqrt(dx * dx + dy * dy);
        }
    }

    xmin -= width;
    ymin -= width;
    xmax += width * 2;
    ymax += width * 2;

    const bbox = {
        'xmin': Math.floor(xmin),
        'ymin': Math.floor(ymin),
        'xmax': Math.ceil(xmax),
        'ymax': Math.ceil(ymax)
    };

    return {
        'bbox': bbox,
        'length': length,
    };
}

function rectangles_intersect(a, b) {
    const result = (
        a.xmin <= b.xmax
        && a.xmax >= b.xmin
        && a.ymin <= b.ymax 
        && a.ymax >= b.ymin
    );

    return result;
}

function stroke_intersects_region(points, bbox) {
    if (points.length === 0) {
        return false;
    }

    const stats = stroke_stats(points, storage.cursor.width);
    return rectangles_intersect(stats.bbox, bbox);
}

function color_to_u32(color_str) {
    const r = parseInt(color_str.substring(0, 2), 16);
    const g = parseInt(color_str.substring(2, 4), 16);
    const b = parseInt(color_str.substring(4, 6), 16);

    return (r << 16) | (g << 8) | b;
}

function color_from_u32(color_u32) {
    const r = (color_u32 >> 16) & 0xFF;
    const g = (color_u32 >> 8) & 0xFF;
    const b = color_u32 & 0xFF;

    let r_str = r.toString(16);
    let g_str = g.toString(16);
    let b_str = b.toString(16);

    if (r <= 0xF) r_str = '0' + r_str;
    if (g <= 0xF) g_str = '0' + g_str;
    if (b <= 0xF) b_str = '0' + b_str;

    return '#' + r_str + g_str + b_str;
}

function ccw(A, B, C) {
    return (C.y - A.y) * (B.x - A.x) > (B.y - A.y) * (C.x - A.x);
}

// https://stackoverflow.com/a/9997374/11420590
function segments_intersect(A, B, C, D) {
    return ccw(A, C, D) != ccw(B, C, D) && ccw(A, B, C) !== ccw(A, B, D);
}

function strokes_intersect_line(x1, y1, x2, y2) {
    const result = [];

    for (const event of storage.events) {
        if (event.type === EVENT.STROKE && !event.deleted) {
            if (event.points.length < 2) {
                continue;
            }

            for (let i = 0; i < event.points.length - 1; ++i) {
                const sx1 = event.points[i].x;
                const sy1 = event.points[i].y;

                const sx2 = event.points[i + 1].x;
                const sy2 = event.points[i + 1].y;

                const A = {'x': x1, 'y': y1};
                const B = {'x': x2, 'y': y2};

                const C = {'x': sx1, 'y': sy1};
                const D = {'x': sx2, 'y': sy2};

                if (segments_intersect(A, B, C, D)) {
                    result.push(event.stroke_id);
                    break;
                }
            }
        }
    }

    return result;
}

function dist_v2(a, b) {
    const dx = a.x - b.x;
    const dy = a.y - b.y;
    return Math.sqrt(dx * dx + dy * dy);
}

function mid_v2(a, b) {
    return {
        'x': (a.x + b.x) / 2.0,
        'y': (a.y + b.y) / 2.0,
    };
}

function perpendicular(ax, ay, bx, by, width) {
    // Place points at (stroke_width / 2) distance from the line
    const dirx = bx - ax;
    const diry = by - ay;
    
    let pdirx = diry;
    let pdiry = -dirx;

    const pdir_norm = Math.sqrt(pdirx * pdirx + pdiry * pdiry);

    pdirx /= pdir_norm;
    pdiry /= pdir_norm;

    return {
        'p1': {
            'x': ax + pdirx * width / 2,
            'y': ay + pdiry * width / 2,
        },

        'p2': {
            'x': ax - pdirx * width / 2,
            'y': ay - pdiry * width / 2,
        }
    };
}