Module: Moon::SAT::Helper

Included in:
Moon::SAT
Defined in:
lib/moon/packages/physics/sat.rb

Constant Summary collapse

T_VECTORS =
`Array.new(10) { Moon::Vector2.zero }`
T_ARRAYS =
`Array.new(5)  { [] }`
T_RESPONSE =
`Response.new`
UNIT_SQUARE =
`Box.new(Moon::Vector2.zero, 1, 1).to_polygon`
LEFT_VORNOI_REGION =
`-1`
MIDDLE_VORNOI_REGION =
`0`
RIGHT_VORNOI_REGION =
`1`

Instance Method Summary collapse

• Check whether two convex polygons are separated by the specified axis (must be a unit vector).

• Check if a point is inside a circle.

• Check if a point is inside a convex polygon.

• Check if two circles collide.

• Check if a circle and a polygon collide.

• Check if a polygon and a circle collide.

• Checks whether polygons collide.

• Calculates which Vornoi region a point is on a line segment.

Instance Method Details

#flatten_points_on(points, normal, result) ⇒ Object

 ``` 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201``` ```# File 'lib/moon/packages/physics/sat.rb', line 185 def flatten_points_on(points, normal, result) min = -0xFFFF max = 0xFFFF points.each_with_index do |p, i| dot = p.dot(normal) if dot < min min = dot end if dot > max max = dot end end result[0] = min result[1] = max end```

#is_separating_axis?(a_pos, b_pos, a_points, b_points, axis, response) ⇒ Boolean

Check whether two convex polygons are separated by the specified axis (must be a unit vector).

 ``` 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284``` ```# File 'lib/moon/packages/physics/sat.rb', line 217 def is_separating_axis?(a_pos, b_pos, a_points, b_points, axis, response) range_a = T_ARRAYS.pop range_b = T_ARRAYS.pop # The magnitude of the offset between the two polygons #offset_v = T_VECTORS.pop.set(b_pos).sub(a_pos) offset_v = T_VECTORS.pop.set(b_pos) - a_pos projected_offset = offset_v.dot(axis) # Project the polygons onto the axis. flatten_points_on(a_points, axis, range_a) flatten_points_on(b_points, axis, range_b) # Move B's range to its position relative to A. range_b[0] += projected_offset range_b[1] += projected_offset # Check if there is a gap. If there is, this is a separating axis and we can stop if range_a[0] > range_b[1] || range_b[0] > range_a[1] T_VECTORS.push(offset_v) T_ARRAYS.push(range_a) T_ARRAYS.push(range_b) return true end # This is not a separating axis. If we're calculating a response, calculate the overlap. if response overlap = 0 # A starts further left than B if range_a[0] < range_b[0] response.a_in_b = false # A ends before B does. We have to pull A out of B if range_a[1] < range_b[1] overlap = range_a[1] - range_b[0] response.b_in_a = false # B is fully inside A. Pick the shortest way out. else option1 = range_a[1] - range_b[0] option2 = range_b[1] - range_a[0] overlap = option1 < option2 ? option1 : -option2 end # B starts further left than A else response.b_in_a = false # B ends before A ends. We have to push A out of B if range_a[1] > range_b[1] overlap = range_a[0] - range_b[1] response.a_in_b = false # A is fully inside B. Pick the shortest way out. else option1 = range_a[1] - range_b[0] option2 = range_b[1] - range_a[0] overlap = option1 < option2 ? option1 : -option2 end end # If this is the smallest amount of overlap we've seen so far, set it as the minimum overlap. abs_overlap = overlap.abs if abs_overlap < response.overlap response.overlap = abs_overlap response.overlap_n.set(axis) if overlap < 0 response.overlap_n.reverse end end end T_VECTORS.push(offset_v) T_ARRAYS.push(range_a) T_ARRAYS.push(range_b) false end```

#point_in_circle(p, c) ⇒ Boolean

Check if a point is inside a circle.

 ``` 325 326 327 328 329 330 331 332``` ```# File 'lib/moon/packages/physics/sat.rb', line 325 def point_in_circle(p, c) difference_v = T_VECTORS.pop.set(p) - c.position radius_sq = c.r * c.r distance_sq = difference_v.lengthsq T_VECTORS.push(difference_v) # If the distance between is smaller than the radius then the point is inside the circle. distance_sq <= radius_sq end```

#point_in_polygon(p, poly) ⇒ Boolean

Check if a point is inside a convex polygon.

 ``` 340 341 342 343 344 345 346``` ```# File 'lib/moon/packages/physics/sat.rb', line 340 def point_in_polygon(p, poly) UNIT_SQUARE.position.set(p) T_RESPONSE.clear result = test_polygon_polygon(UNIT_SQUARE, poly, T_RESPONSE) result = T_RESPONSE.a_in_b if result result end```

#test_circle_circle(a, b, response) ⇒ Boolean

Check if two circles collide.

 ``` 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380``` ```# File 'lib/moon/packages/physics/sat.rb', line 355 def test_circle_circle(a, b, response) # Check if the distance between the centers of the two # circles is greater than their combined radius. difference_v = T_VECTORS.pop.set(b.position) - a.position total_radius = a.r + b.r total_radius_sq = total_radius * total_radius distance_sq = difference_v.lengthsq # If the distance is bigger than the combined radius, they don't intersect. if distance_sq > total_radius_sq T_VECTORS.push(difference_v) return false end # They intersect. If we're calculating a response, calculate the overlap. if response dist = Math.sqrt(distance_sq) response.a = a response.b = b response.overlap = total_radius - dist response.overlap_n = difference_v.normalize response.overlap_v = difference_v * response.overlap response.a_in_b = a.r <= b.r && dist <= b.r - a.r response.b_in_a = b.r <= a.r && dist <= a.r - b.r end T_VECTORS.push(difference_v) return true end```

#test_circle_polygon(circle, polygon, response) ⇒ boolean

Check if a circle and a polygon collide.

*NOTE:* This is slightly less efficient than polygonCircle as it just runs polygonCircle and reverses everything at the end.

 ``` 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543``` ```# File 'lib/moon/packages/physics/sat.rb', line 528 def test_circle_polygon(circle, polygon, response) # Test the polygon against the circle. result = test_polygon_circle(polygon, circle, response) if result && response # Swap A and B in the response. a = response.a a_in_b = response.a_in_b response.overlap_n = -response.overlap_n response.overlap_v = -response.overlap_v response.a = response.b response.b = a response.a_in_b = response.b_in_a response.b_in_a = a_in_b end result end```

#test_polygon_circle(polygon, circle, response) ⇒ boolean

Check if a polygon and a circle collide.

 ``` 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516``` ```# File 'lib/moon/packages/physics/sat.rb', line 389 def test_polygon_circle(polygon, circle, response) # Get the position of the circle relative to the polygon. circle_pos = T_VECTORS.pop.set(circle.position - polygon.position) radius = circle.r radius2 = radius * radius points = polygon.calc_points len = points.size edge = T_VECTORS.pop point = T_VECTORS.pop # For each edge in the polygon: points.size.times do |i| nxt = i == len - 1 ? 0 : i + 1 prev = i == 0 ? len - 1 : i - 1 overlap = 0 overlap_n = nil # Get the edge. edge.set(polygon.edges[i]) # Calculate the center of the circle relative to the starting point of the edge. point.set(circle_pos - points[i]) # If the distance between the center of the circle and the point # is bigger than the radius, the polygon is definitely not fully in # the circle. if response && point.lengthsq > radius2 response.a_in_b = false end # Calculate which Vornoi region the center of the circle is in. region = vornoi_region(edge, point) # If it's the left region: if region == LEFT_VORNOI_REGION # We need to make sure we're in the RIGHT_VORNOI_REGION of the previous edge. edge.set(polygon.edges[prev]) # Calculate the center of the circle relative the starting point of the previous edge point2 = T_VECTORS.pop.set(circle_pos - points[prev]) region = vornoi_region(edge, point2) if region == RIGHT_VORNOI_REGION # It's in the region we want. Check if the circle intersects the point. dist = point.length if dist > radius # No intersection T_VECTORS.push(circle_pos) T_VECTORS.push(edge) T_VECTORS.push(point) T_VECTORS.push(point2) return false elsif response # It intersects, calculate the overlap. response.b_in_a = false overlap_n = point.normalize overlap = radius - dist end end T_VECTORS.push(point2) # If it's the right region: elsif region == RIGHT_VORNOI_REGION # We need to make sure we're in the left region on the next edge edge.set(polygon.edges[nxt]) # Calculate the center of the circle relative to the starting point of the next edge. point.set(circle_pos - points[nxt]) region = vornoi_region(edge, point) if region == LEFT_VORNOI_REGION # It's in the region we want. Check if the circle intersects the point. dist = point.length if dist > radius # No intersection T_VECTORS.push(circle_pos) T_VECTORS.push(edge) T_VECTORS.push(point) return false elsif response # It intersects, calculate the overlap. response.b_in_a = false overlap_n = point.normalize overlap = radius - dist end end # Otherwise, it's the middle region: else # Need to check if the circle is intersecting the edge, # Change the edge into its "edge normal". normal = edge.perp.normalize # Find the perpendicular distance between the center of the # circle and the edge. dist = point.dot(normal) dist_abs = Math.abs(dist) # If the circle is on the outside of the edge, there is no intersection. if dist > 0 && dist_abs > radius # No intersection T_VECTORS.push(circle_pos) T_VECTORS.push(normal) T_VECTORS.push(point) return false elsif response # It intersects, calculate the overlap. overlap_n = normal overlap = radius - dist # If the center of the circle is on the outside of the edge, or part of the # circle is on the outside, the circle is not fully inside the polygon. if dist >= 0 || overlap < 2 * radius response.b_in_a = false end end end # If this is the smallest overlap we've seen, keep it. # (overlap_n may be nil if the circle was in the wrong Vornoi region). if overlap_n && response && overlap.abs < response.overlap.abs response.overlap = overlap response.overlap_n.set(overlap_n) end end # Calculate the final overlap vector - based on the smallest overlap. if response response.a = polygon response.b = circle response.overlap_v = response.overlap_n * response.overlap end T_VECTORS.push(circle_pos) T_VECTORS.push(edge) T_VECTORS.push(point) true end```

#test_polygon_polygon(a, b, response) ⇒ boolean

Checks whether polygons collide.

 ``` 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576``` ```# File 'lib/moon/packages/physics/sat.rb', line 552 def test_polygon_polygon(a, b, response) a_points = a.calc_points b_points = b.calc_points # If any of the edge normals of A is a separating axis, no intersection. a.normals.each_with_index do |normal, i| if is_separating_axis?(a.position, b.position, a_points, b_points, normal, response) return false end end # If any of the edge normals of B is a separating axis, no intersection. b.normals.each_with_index do |normal, i| if is_separating_axis?(a.position, b.position, a_points, b_points, normal, response) return false end end # Since none of the edge normals of A or B are a separating axis, there is an intersection # and we've already calculated the smallest overlap (in is_separating_axis?). Calculate the # final overlap vector. if response response.a = a response.b = b response.overlap_v.set(response.overlap_n * response.overlap) end return true end```

#vornoi_region(line, point) ⇒ Moon::Numeric

Calculates which Vornoi region a point is on a line segment. It is assumed that both the line and the point are relative to `(0,0)`

``````       |       (0)      |
(-1)  [S]--------------[E]  (1)
|       (0)      |
``````
 ``` 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318``` ```# File 'lib/moon/packages/physics/sat.rb', line 303 def vornoi_region(line, point) lengthsq = line.lengthsq dp = point.dot(line) # If the point is beyond the start of the line, it is in the # left vornoi region. if dp < 0 LEFT_VORNOI_REGION # If the point is beyond the end of the line, it is in the # right vornoi region. elsif dp > lengthsq RIGHT_VORNOI_REGION # Otherwise, it's in the middle one. else MIDDLE_VORNOI_REGION end end```