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 rdp_find_max(state, points, start, end) {
    const EPS = 0.5 / Math.pow(state.canvas.zoom, 0.25);
    // 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 strokes_intersect_line(state, a, b) {
    // TODO: handle stroke / eraser width
    const result = [];

    for (let i = 0; i < state.events.length; ++i) {
        const event = state.events[i];
        if (event.type === EVENT.STROKE && !event.deleted) {
            for (let i = 0; i < event.points.length - 1; ++i) {
                const c = event.points[i + 0];
                const d = event.points[i + 1];

                if (segments_intersect(a, b, c, d)) {
                    result.push(i);
                    break;
                }
            }
        }
    }

    return result;
}

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 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 point_in_quad(p, quad_topleft, quad_bottomright) {
    if ((quad_topleft.x <= p.x && p.x < quad_bottomright.x) && (quad_topleft.y <= p.y && p.y < quad_bottomright.y)) {
        return true;
    }

    return false;
}

function segment_interesects_quad(a, b, quad_topleft, quad_bottomright, quad_topright, quad_bottomleft) {
    if (point_in_quad(a, quad_topleft, quad_bottomright)) {
        return true;
    }

    if (point_in_quad(b, quad_topleft, quad_bottomright)) {
        return true;
    }

    if (segments_intersect(a, b, quad_topleft, quad_topright)) return true;
    if (segments_intersect(a, b, quad_topright, quad_bottomright)) return true;
    if (segments_intersect(a, b, quad_bottomright, quad_bottomleft)) return true;
    if (segments_intersect(a, b, quad_bottomleft, quad_topleft)) return true;

    return false;
}

function stroke_bbox(points) {
    let min_x = points[0].x;
    let max_x = min_x;

    let min_y = points[0].y;
    let max_y = min_y;

    for (const p of points) {
        min_x = Math.min(min_x, p.x);
        min_y = Math.min(min_y, p.y);
        max_x = Math.max(max_x, p.x);
        max_y = Math.max(max_y, p.y);
    }

    return {'x1': min_x, 'y1': min_y, 'x2': max_x, 'y2': max_y};
}

function quad_onscreen(screen, bbox) {
    if (screen.x1 < bbox.x2 && screen.x2 > bbox.x1 && screen.y2 > bbox.y1 && screen.y1 < bbox.y2) {
        return true;
    }

    return false;
}

function segments_onscreen(state, context) {
    const result = [];
    const screen_topleft = screen_to_canvas(state, {'x': 0, 'y': 0});
    const screen_bottomright = screen_to_canvas(state, {'x': context.canvas.width, 'y': context.canvas.height});
    const screen_topright = { 'x': screen_bottomright.x, 'y': screen_topleft.y };
    const screen_bottomleft = { 'x': screen_topleft.x, 'y': screen_bottomright.y };
    const screen = {'x1': screen_topleft.x, 'y1': screen_topleft.y, 'x2': screen_bottomright.x, 'y2': screen_bottomright.y};

    let head = 0;

    for (let i = 0; i < state.events.length; ++i) {
        const event = state.events[i];
        if (event.type === EVENT.STROKE && !event.deleted) {
            if (quad_onscreen(screen, event.bbox)) {
                for (let j = 0; j < event.points.length - 1; ++j) {
                    const a = event.points[j + 0];
                    const b = event.points[j + 1];

                    if (segment_interesects_quad(a, b, screen_topleft, screen_bottomright, screen_topright, screen_bottomleft)) {
                        let base = head + j * 4;
                        // We draw quads as [1, 2, 3, 4, 3, 2]
                        result.push(base + 0, base + 1, base + 2);
                        result.push(base + 3, base + 2, base + 1);
                    }
                }
            }
            head += (event.points.length - 1) * 4;
        }
    }

    return result;
}