Better readability for SAT demo
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@ -6,6 +6,40 @@ from ..math import *
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from ..draw import *
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def compute_separating_axes(p1, p2):
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"""Compute the projections upon the separating axes of polygons p1 and p2.
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For efficient collision detection, this could early-exit as soon as one
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axis is found where the projections of p1 and p2 do not overlap. For
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visualization purposes, we compute the projections for all axes and
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return the results."""
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# The list of axes to project upon
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axes = []
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# Iterate the normals of both polygons
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for normal in p1.get_normals() + p2.get_normals():
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# we can trim out normals that are in the same or opposite direction
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# as axes we already have, since they will give us the same overlap
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# information
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if not any(is_colinear(*normal, *axis) for axis in axes):
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axes.append(normal)
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# helper function to find the min/max projections of vertices onto
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# the given axis.
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def get_min_max(axis, vertices):
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projections = [dot(*axis, *vertex) for vertex in vertices]
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return min(projections), max(projections)
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return [
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(axis,
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get_min_max(axis, p1.get_translated_vertices()),
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get_min_max(axis, p2.get_translated_vertices()))
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for axis in axes
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]
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class SeparatingAxisTheorem:
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title = "Separating Axis Theorem"
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@ -19,6 +53,7 @@ class SeparatingAxisTheorem:
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self.generate_shape2()
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def generate_shape2(self):
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"""Generates the shape we can move around - a regular polygon."""
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rotation = 45 if self.shape2 is None else self.shape2.rotation
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self.shape2 = generate_polygon(*get_cursor_pos(),
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rotation,
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@ -27,9 +62,11 @@ class SeparatingAxisTheorem:
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def handle_key_down(self, key):
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if key == pygame.K_a:
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# remove a side from the polygon
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self.shape2_sides = max(self.shape2_sides - 1, 3)
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self.generate_shape2()
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if key == pygame.K_d:
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# add a side to the polygon
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self.shape2_sides = min(self.shape2_sides + 1, 31)
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self.generate_shape2()
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@ -38,77 +75,65 @@ class SeparatingAxisTheorem:
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inputs = get_inputs()
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if inputs[pygame.K_q]:
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# rotate counter-clockwise by 90 degrees every second
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self.shape2.rotate((1/60) * -90)
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if inputs[pygame.K_e]:
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# same as above, but clockwise
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self.shape2.rotate((1/60) * 90)
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def draw_axis(self, surface, normal, overlap, min1, max1, min2, max2):
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offset = scale(*rnormal(*normal), 300)
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colliding = overlap < 0
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if not colliding:
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# separating line
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dist = scale(*normal,
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(min1 if min1 > min2 else min2) - overlap * 0.5)
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line(surface, CYAN,
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add(*dist, *offset),
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add(*dist, *scale(*lnormal(*normal), 1000)))
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# axis
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line(surface, WHITE,
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add(*scale(*reverse(*normal), 1000), *offset),
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add(*scale(*normal, 1000), *offset))
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# shape 1
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line(surface, GREEN if not colliding else RED,
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add(*scale(*normal, min1), *offset),
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add(*scale(*normal, max1), *offset), 8)
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# shape 2
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line(surface, GREEN if not colliding else RED,
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add(*scale(*normal, min2), *offset),
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add(*scale(*normal, max2), *offset), 8)
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def render(self, surface):
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self.handle_input()
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normals = []
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gaps = []
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def add_if_not_exists(normal):
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for existing in normals:
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if is_colinear(*existing, *normal):
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return
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normals.append(normal)
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for result in compute_separating_axes(self.shape1, self.shape2):
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for normal in self.shape1.get_normals() + self.shape2.get_normals():
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add_if_not_exists(normal)
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axis, (min1, max1), (min2, max2) = result
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def get_min_max(normal, vertices):
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_min = float('inf')
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_max = float('-inf')
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for vertex in vertices:
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proj = dot(*normal, *vertex)
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_min = min(_min, proj)
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_max = max(_max, proj)
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return _min, _max
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# length of the gap between the two projections
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gap = max(min2 - max1, min1 - max2)
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gaps.append(gap)
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overlaps = []
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for normal in normals:
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min1, max1 = get_min_max(normal,
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self.shape1.get_translated_vertices())
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min2, max2 = get_min_max(normal,
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self.shape2.get_translated_vertices())
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self.draw_axis(surface, axis, gap, min1, max1, min2, max2)
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overlap = max(min2 - max1, min1 - max2)
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overlaps.append(overlap)
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self.draw_axis(surface, normal, overlap,
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min1, max1, min2, max2)
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colliding = all(overlap < 0 for overlap in overlaps)
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colliding = all(gap < 0 for gap in gaps)
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if colliding:
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text_screen(surface, WHITE, (10, HEIGHT - 20),
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f"Min Distance to Resolve: {max(overlaps)}")
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f"Min Distance to Resolve: {max(gaps)}")
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self.shape1.draw(surface, YELLOW, 1)
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self.shape2.draw(surface, RED if colliding else WHITE, 1)
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def draw_axis(self, surface, normal, gap, min1, max1, min2, max2):
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"""Draws a separating axis with shape projections, and separating line.
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Uses colours to clearly indicate whether the projections overlap."""
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# since the normal's origin is 0,0 (center of the screen), calcuate
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# an offset to move all drawing off to one side - in this case 300px.
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offset = scale(*rnormal(*normal), 300)
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overlapping = gap < 0
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if not overlapping:
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# how far from the center of the gap is from the origin
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dist = scale(*normal, (min1 if min1 > min2 else min2) - 0.5 * gap)
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# the separating line
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line(surface, CYAN,
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add(*dist, *offset),
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add(*dist, *scale(*lnormal(*normal), 1000)))
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# axis, extending off the screen in both directions
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line(surface, WHITE,
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add(*offset, *scale(*reverse(*normal), 1000)),
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add(*offset, *scale(*normal, 1000)))
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# projection 1
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line(surface, RED if overlapping else GREEN,
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add(*offset, *scale(*normal, min1)),
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add(*offset, *scale(*normal, max1)), 8)
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# projection 2
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line(surface, RED if overlapping else GREEN,
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add(*offset, *scale(*normal, min2)),
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add(*offset, *scale(*normal, max2)), 8)
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