From 7f33e917d7e2aa1b451424eaf3b58424599138c8 Mon Sep 17 00:00:00 2001
From: Matt Low <matt@mlow.ca>
Date: Sat, 14 Nov 2020 22:12:00 +0400
Subject: [PATCH] Add Separating Axis Theorum demo

---
 geom/demos/sat.py | 77 +++++++++++++++++++++++++++++++++++++++++++++++
 geom/screen.py    |  3 +-
 2 files changed, 79 insertions(+), 1 deletion(-)
 create mode 100644 geom/demos/sat.py

diff --git a/geom/demos/sat.py b/geom/demos/sat.py
new file mode 100644
index 0000000..5f94946
--- /dev/null
+++ b/geom/demos/sat.py
@@ -0,0 +1,77 @@
+from ..geom import Rect, Polygon
+from .. import WIDTH, HEIGHT, get_cursor_pos
+from ..colors import *
+from ..math import *
+from ..draw import *
+
+class SeparatingAxisTheorem:
+
+    title = "Separating Axis Theorem"
+
+    def __init__(self):
+        self.shape1 = Polygon(0, 0, [
+            (0, 60),
+            (60, 0),
+            (0, -60),
+            (-60, 0)
+        ])
+
+        self.shape2 = Polygon(*get_cursor_pos(), [
+            (60, 60),
+            (60, -60),
+            (-60, -60),
+            (-60, 60)
+        ])
+
+    def render(self, surface):
+        self.shape2.set_position(*get_cursor_pos())
+
+        normals = []
+
+        def add_if_not_exists(normal):
+            for existing in normals:
+                if is_equal(*existing, *normal):
+                    return
+            normals.append(normal)
+
+        for normal in self.shape1.get_normals() + self.shape2.get_normals():
+            add_if_not_exists(normal)
+
+        def get_min_max(normal, vertices):
+            _min = float('inf')
+            _max = float('-inf')
+            for vertex in vertices:
+                proj = dot(*normal, *vertex)
+                _min = min(_min, proj)
+                _max = max(_max, proj)
+            return _min, _max
+
+        collisions = []
+        for normal in normals:
+            min1, max1 = get_min_max(normal,
+                                     self.shape1.get_translated_vertices())
+            min2, max2 = get_min_max(normal,
+                                     self.shape2.get_translated_vertices())
+
+            colliding = max1 > min2 and max2 > min1
+            collisions.append(colliding)
+
+            offset = scale(*rnormal(*normal), 300)
+
+            # axis
+            line(surface, WHITE,
+                 add(*scale(*reverse(*normal), 1000), *offset),
+                 add(*scale(*normal, 1000), *offset))
+
+            # shape 1
+            line(surface, YELLOW if not colliding else RED,
+                      add(*scale(*normal, min1), *offset),
+                      add(*scale(*normal, max1), *offset), 5)
+            # shape 2
+            line(surface, YELLOW if not colliding else RED,
+                      add(*scale(*normal, min2), *offset),
+                      add(*scale(*normal, max2), *offset), 5)
+
+
+        self.shape1.draw(surface, YELLOW, 4)
+        self.shape2.draw(surface, RED if all(collisions) else WHITE, 4)
diff --git a/geom/screen.py b/geom/screen.py
index 4b2a1bd..5017ce8 100644
--- a/geom/screen.py
+++ b/geom/screen.py
@@ -1,5 +1,5 @@
 import pygame
-from .demos import aabb, vec_proj
+from .demos import aabb, vec_proj, sat
 from . import HEIGHT
 from .colors import *
 from .draw import text_screen
@@ -11,6 +11,7 @@ class Screen:
             vec_proj.VecProj(),
             aabb.AABBDistance(),
             aabb.PointAABBDistance(),
+            sat.SeparatingAxisTheorem(),
         ]
         self.demo = 0