mjestecko/articles/2d-visibility/page.mmd

Title:  2D Visibility
Brief:  Visibility triangles from 2D occluding segment geometry in GDScript.
Date:   1686547796
Tags:   Programming, Godot, GDScript
CSS:    /style.css

![](/articles/2d-visibility/example.gif)

Based on [Redblobgames' visibility article and Haxe reference implementation](https://www.redblobgames.com/articles/visibility)

Full usable code is [here](/articles/2d-visibility/Visibility2D.gd.txt).

### Explanation ###

First step is determining angles for each segment point as well as denoting
which one gets encountered first.

```gdscript
for segment in range(0, _endpoints.size(), 2):
    var p1 := _endpoints[segment] as EndPoint
    var p2 := _endpoints[segment + 1] as EndPoint
    p1.angle = (p1.point - center).angle()
    p2.angle = (p2.point - center).angle()
    var da := p2.angle - p1.angle
    if da <= PI: da += TAU
    if da > PI: da -= TAU
    p1.begin = da > 0.0
    p2.begin = not p1.begin
```

Then points are sorted by angle and beginning:

```gdscript
static func sort(p_a: EndPoint, p_b: EndPoint) -> bool:
    if p_a.angle > p_b.angle: return true
    elif p_a.angle < p_b.angle: return false
    elif not p_a.begin and p_b.begin: return true
    else: return false
```

Then in two passes:
- Walk over sorted points.
- When nearest segment end or another more nearest encountered, -
remember the starting angle and only emit two points representing the visible portion of segment on second pass.

```gdscript
var start_angle := 0.0

for n_pass in range(2):
    for p_idx in range(_sorted_endpoints.size() - 1, -1, -1):
        var p := _sorted_endpoints[p_idx] as EndPoint
        var old := -1 if _open.empty() else _open[0]

        if p.begin:
            var idx := 0
            while idx < _open.size() and _is_segment_in_front(p.segment, _open[idx]):
                idx += 1
            _open.insert(idx, p.segment)
        else:
            var idx := _open.rfind(p.segment)
            if idx != -1: _open.remove(idx)

        if old != (-1 if _open.empty() else _open[0]):
            if n_pass == 1:
                var p3 := _endpoints[old].point as Vector2 if old != -1 else \
                    center + Vector2(cos(start_angle), sin(start_angle)) * 500.0
                var t2 := Vector2(cos(p.angle), sin(p.angle))
                var p4 := p3.direction_to(_endpoints[old + 1].point) if old != -1 else t2 

                # note: Checks are in case of parallel lines.
                var l = Geometry.line_intersects_line_2d(p3, p4, center,
                    Vector2(cos(start_angle), sin(start_angle)))
                if l != null: output.append(l)
                l = Geometry.line_intersects_line_2d(p3, p4, center, t2)
                if l != null: output.append(l)

            start_angle = p.angle
```

Where segment front deciding algorithm is as follows, using cross products:

```gdscript
func _is_segment_in_front(p_segment1: int, p_segment2: int) -> bool:
    var s1p1 := _endpoints[p_segment1].point as Vector2
    var s1p2 := _endpoints[p_segment1 + 1].point as Vector2
    var s2p1 := _endpoints[p_segment2].point as Vector2
    var s2p2 := _endpoints[p_segment2 + 1].point as Vector2

    var d := s1p2 - s1p1
    var p := s2p1.linear_interpolate(s2p2, 0.01)
    var a1 := (d.x * (p.y - s1p1.y) \
             - d.y * (p.x - s1p1.x)) < 0.0
    p = s2p2.linear_interpolate(s2p1, 0.01)
    var a2 := (d.x * (p.y - s1p1.y) \
             - d.y * (p.x - s1p1.x)) < 0.0
    var a3 := (d.x * (center.y - s1p1.y) \
             - d.y * (center.x - s1p1.x)) < 0.0

    if a1 == a2 and a2 == a3: return true

    d = s2p2 - s2p1
    p = s1p1.linear_interpolate(s1p2, 0.01)
    var b1 := (d.x * (p.y - s2p1.y) \
             - d.y * (p.x - s2p1.x)) < 0.0
    p = s1p2.linear_interpolate(s1p1, 0.01)
    var b2 := (d.x * (p.y - s2p1.y) \
             - d.y * (p.x - s2p1.x)) < 0.0
    var b3 := (d.x * (center.y - s2p1.y) \
             - d.y * (center.x - s2p1.x)) < 0.0

    return b1 == b2 and b2 != b3
```

### Usage example ###
Visibility2D.gd class implements builder interface to make it slightly easier to work with.

```gdscript
func _process(_delta):
    $Visibility2D.init_builder() \
        .view_point(get_global_mouse_position()) \
        .bounds(get_viewport_rect()) \
        .occluder($Line2D) \
        .finalize()

    for child in $Cones.get_children():
        child.queue_free()

    var edges = $Visibility2D.sweep()
    for i in range(0, edges.size() - 1, 2):
        var polygon := Polygon2D.new()
        polygon.polygon = PoolVector2Array([$Visibility2D.center, edges[i], edges[i + 1]])
        $Cones.add_child(polygon)
```