swfchan: FITC_beyondHittest07.swf (info)

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Beyond hitTest(): proper collision detection in actionscript

METANET SOFTWARE

One of the most important features of any action game is collision; sadly it is usually one of the
weakest points in most flash games. One reason for this is that many programmers rely upon the built-
in hitTest() method, which is extremely limited: it works only with axis-aligned rectangles or points, and
returns only a boolean result.
While a simple yes/no result is sufficient in some cases, many applications (like racing games) really
do require extra information about collisions when they occur, in order to respond to the collision in a
meaningful way. Often this extra information is implicitly found by testing multiple positions for
collision, in order to infer information about the collision; from several yes/no results, a more detailed
model of what’s happening can be built. However, this awkward (ab)use of the built-in collision
functions undermines the entire process – if you need to hitTest() multiple times (at different points) for
each collision, the built-in methods cease to outperform “real” collision detection methods. It’s time to
think about doing it the right way.
This presentation will introduce some useful tools for solving the collision problem quickly and
accurately, including use of the seperating-axis-theorem to test two shapes, as well as higher-level
data structures and approaches which will reduce the number of tests needed.

download this presentation at:
http://www.harveycartel.org/metanet/tutorials/fitc05.zip

** WARNING! **
may contain programmer art

"The Curse of Sylvaniah"
(by Strille and LuxRegina)

Collision Detection can be a complex problem, however
it is also a well-researched problem.

Game Programming

Collision Detection

Physics

Graphics

Game Rules

Games which benefit from complex collision detection:

-Racing

-Pool, Pinball

-Basketball

-Platform/Run-and-Jump

-Pool

-Basketball

even better: New Genres!!

Collision Detection == Gameplay Options

hitTest()

-only returns a boolean result

-only works with axis-aligned rectangles

Collision responses using hitTest():

BOOM!

Destroy

Reset

Reverse

Collision responses we'd like to support:

Friction / Bounce

Resolving Penetration

Orient-to-Surface

Collision Shapes Supported by hitTest():

Collision Shapes we'd like to support:

maybe I'm not using hitTest() "properly"?

..these sort of "solutions" are slow and buggy.

hitTest(): Cutting-edge Technology

..from the arcades of the 80s

Physics: "the new graphics"

..it doesn't have to be complicated or slow, even in actionscript.

position += velocity;

newpos = oldpos + vel;

physics

Trig

Vectors

SNES

graphical power

processing power

<4MHz

64k

16bit integers

>2GHz

512MB

64bit floats

Flash

vs.

Game Developer's Conference 2005:

-gameplay is becomming more important than graphics

Collision Detection and Physics are
powerful tools for creating unique gameplay.

Gish
by Chronic Logic
http://www.chroniclogic.com

Break Quest
by Nurium Games
www.nurium.com

Soldat
by Michal Marcinkowski
www.soldat.pl

Katamari Damacy
by Keita Takahashi / Namco
http://www.namco.com/games
/katamari_damacy/

Beyond hitTest() part 0:
Collision Response

-friction

-bounce

-sliding

-etc.

Penetration Vector

Penetration Amount

Penetration Direction

= Penetration Vector

* Penetration Amount

Collision Direction

Collision Velocity

Velocity Perpendicular
to Surface

Velocity Parallel
to Surface

Friction and Bounce:

Beyond hitTest() part 1:
Narrow-Phase Collision Detection
(a.k.a object-vs-object)

Collision Detection:

-are these two shapes colliding?

-if so, how are they colliding?
(i.e what is the penetration vector?)

-for all possibly colliding pairs of shapes:

broad phase

narrow phase

the Method of Separating Axes

axis == direction

the Method of Seperating Axes

this method is based on the Separating Axis Theorem (SAT)

the SAT applies to all convex shapes:

Separating Axis Theorem: part 1

If two convex polygons don't overlap,
then there exists a direction along
which they are separated.

(the converse is also true:
if there is no separating
direction, the polygons
must be overlapping)

Separating Axis Theorem: part 2

If a separating axis exists, then it
must be perpendicular to an edge
of one of the polygons.

Method of Separating Axes:

determine all potentially separating axes
for(each potentially separating axis):
if(axis separates objects): return false (objects aren't colliding)
else, continue
if(no separating axis found): return true (objects are colliding)

"Vector Math"

Vectors

point0 = (x0,y0)
point1 = (x1,y1)
vector from p1 to p0 = (x0-x1, y0-y1)

vx = x0 - x1;
vy = y0 - y1;

Unit Vectors
a.k.a Direction Vectors

vector0 = (vx,vy)
len = length of vector0
direction vector parallel to vector0 =
(vx/len, vy/len)

len = Math.sqrt(vx*vx + vy*vy);
dx = vx/len;
dy = vy/len;

Normal Vectors

vector0 = (vx,vy)
lefthand normal = (vy,-vx)
righthand normal = (-vy,vx)
lefthand normal = -righthand normal

rx = -vy;
ry = vx;
lx = vy;
ly = -vx;

(6,-1)

(1,6)

(-1,-6)

(0,0)

Normal Vectors

-these are the potentially separating axes.

Dot Product

-let A be the vector from p1 to p2
-let B be the vector from p1 to p0
-the dotproduct of A and B is a measure of the
relative directions of two vectors

ax = x2 - x1; //ax,ay is
ay = y2 - y1; //p1->p2
bx = x0 - x1; //bx,by is
by = y0 - y1; //p1->p0
AdotB = ax*bx + ay*by;
//AdotB is the dotprod of
//p1->p2 and p1->p0

the dotproduct of A and B is:
-max when A and B are pointing in the same direction
-min when A and B are pointing in opposite directions
-0 when A and B are perpendicular

-if vector A is unit-legth and vector B
isn't, the dotproduct of A and B is
equivalent ot the length of B when
measured or viewed along the axis
defined by A
-this is how we "project" vectors onto
an axis

ax = x2 - x1;
ay = y2 - y1;
len = Math.sqrt(ax*ax + ay*ay);
ax /= len; //ax,ay is now
ay /= len; //unit-length
bx = x0 - x1;
by = y0 - y1;
AdotB = ax*bx + ay*by;

Vector Projection

(vector A is unit-legth and vector B isn't)
-multiply A by the dotproduct of A and B,
and the result is a vector we call "B
projected onto (the axis defined by) A"

ax = x2 - x1;
ay = y2 - y1;
len = Math.sqrt(ax*ax + ay*ay);
ax /= len;
ay /= len;
bx = x0 - x1;
by = y0 - y1;
AdotB = ax*bx + ay*by;
px = ax*AdotB; //px,py is B
py = ay*AdotB; //projected onto A

-now we can project vectors onto an arbitrary axis
-this is how we'll project collision shapes onto the potentially separating axes

determine all potentially saperating axes
for(each potentially separating axis):
if(axis separates objects): return false (objects aren't colliding)
else, continue
if(no separating axis found): return true (objects are colliding)

this is the step where we project the shapes onto an axis
and look at the results (i.e are objects separated along that axis,
or are they overlapping along that axis?)

Box vs. Box: 4 axes to test

wait a second....

-this seems a bit complicated..

-don't we still end up with only a boolean result?!

the Method of Separating Axes is simply an extension
of everyone's favorite "circle-vs-circle" collision method

Circle-vs-Circle:
a) calculate the distance between circle centers (green line)
b) calculate the sum of the radii of the circles (blue lines)
if the distance between the circles is greater than the sum of their radii,
then the circles are separated (i.e don't overlap).
if the distance between them is less than the sum of their radii, then
the circles overlap.

delta = distance between circles
rad = sum of radii
diff = rad - delta
if(diff < 0): no collision
if(0 <= diff): collision
..AND, we know how to calculate the penetration vector:
penetration amount = diff
penetration direction is parallel to delta

our method is the same as circle-circle, except that:

-we test more than a single axis
-we can't simply look at the "raw" value of radius and distance
measurements; we have to project them onto an axis and look at
the measurements of the projected values

If we do find a collision (i.e if the shapes overlap along all axes), we
use the axis of least overlap as the penetration direction, and the
amount of overlap along that axis as the penetration amount.

we need to know:

which directions are perpendicular to our objects
how to project each object onto an arbitrary axis

Projecting Shapes onto an Axis: Oriented Box

oriented box:
-position px,py
-halfwidths xw,yw
-"facing" vector dx,dy
(defines the x-axis of the box)

find the size of the box when projected onto the axis ax,ay:

function ProjectBox(box,ax,ay)
{
ix = box.xw * box.dx; //dx,dy: the unit vector which points along the x-axis
iy = box.xw * box.dy; //of the box; ix,iy is the x halfwidth vector
jx = box.yw * -box.dy; //-dy,dx: the unit vector which points along the y-axis
jy = box.yw * box.dx; //of the box; jx,jy is the x halfwidth vector
dpi = ix*ax + iy*ay; //project both halfwidth vectors onto the axis
dpj = jx*ax + jy*ay;
bsize = Math.abs(dpi) + Math.abs(dpj);
return bsize; //bsize is the "radius" of the box when projected onto the axis
}

deltax = boxA.px - boxB.px; //deltax,deltay is the vector between the two box centers
deltay = boxA.py - boxB.py;
axis_x = boxA.dx; //test boxA's x-axis (boxA.dx, boxA.dy)
axis_y = boxA.dy;
asize = boxA.xw; //the size of A when projected onto its own x-axis is its x-width
bsize = ProjectBox(boxB, axis_x, axis_y); //project B onto the axis
dsize = Math.abs(deltax*axis_x + deltay*axis_y);
penAx = (asize + bsize) - dsize;
if(0 < penAx)
{
//boxes overlap along axis; check next axis
axis_x = boxB.dx; //test boxB's x-axis (boxB.dx, boxB.dy)
axis_y = boxB.dy;
asize = ProjectBox(boxA, axis_x, axis_y);//project B onto the axis
bsize = boxB.xw;
dsize = Math.abs(deltax*axis_x + deltay*axis_y);
penBx = (asize + bsize) - dsize;
if(0 < penBx)
{
//boxes overlap along axis; check next axis
<...test the other 2 axes here...>
}
else
{
//boxes don't overlap
}
}
else
{
//boxes don't overlap
}

What wasn't mentioned:

-tracking the axis of minimum overlap
-which way (along the axis of minimum overlap) we should project

Please visit our online tutorials for source code and
a more in-depth look at the process.

..what about circles?

..what about shapes that aren't convex?

(original diagram by Gino Van Den Bergen)

Optimisations?
preprocess, preprocess, preprocess

Questions about SAT/MSA?

Beyond hitTest() part 2:
Broad-Phase Collision Detection
(a.k.a spatial databases)

Bounding Boxes

Better Solutions: Uniform Grid

Better Solutions: Quadtree

Any spatial database must support the following
operations:

Neighborhood Query:
quickly determine which objects are near a given position

Update:
updating the database to reflect changes to object positions

Grids

vs.

Trees

fast query/update

slow query/update

needs lots of memory

needs less memory

Grids:

2D: 200x100 tiles @ 256bytes = 5MB
3D: 200x100x100 tiles @ 256bytes = 500MB

We can afford the extra memory, but not the extra processor time.

Finding the cell which contains point px,py:

grid_column = Math.floor(px / cell_width);
grid_row = Math.floor(py / cell_height);

Colliding objects vs. each other

Regular Grid

Loose Grid

-faster query (less cells to look in)
-slower update (more cells to update)

-slower query (more cells to look in)
-faster update (less cells to update)

Colliding objects vs. "the world"

Tiles:

Linesegs:

Raycasting

-simpler than you might think
-useful for modelling bullets or line-of-sight/vision tests

-there are many algorithms for marching
through a grid along a ray; we use this one

-this is the core of the algorithm:
only 10 lines of code

THE END.. Questions?

In case you we sleeping:
-collision detection is a useful tool for making fun games
-the Method of Separating Axes is a useful tool for narrow-phase
collision detection
-a uniform grid is a useful tool for broad-phase collision detection

Source code (and tutorials) for almost everything mentioned is
available free from our website: http://www.harveycartel.org/metanet/

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Symbol 172 Text	Uses:3	Used by:176
Symbol 173 Text	Uses:3	Used by:176
Symbol 174 Text	Uses:3	Used by:176
Symbol 175 Text	Uses:3	Used by:176
Symbol 176 MovieClip	Uses:171 172 173 174 175	Used by:Timeline
Symbol 177 Text	Uses:3	Used by:Timeline
Symbol 178 Text	Uses:3	Used by:Timeline
Symbol 179 Bitmap	Used by:180
Symbol 180 Graphic	Uses:179	Used by:Timeline
Symbol 181 Text	Uses:3	Used by:Timeline
Symbol 182 Text	Uses:3	Used by:Timeline
Symbol 183 Text	Uses:163	Used by:Timeline
Symbol 184 Text	Uses:3	Used by:Timeline
Symbol 185 Text	Uses:3	Used by:Timeline
Symbol 186 Text	Uses:163	Used by:Timeline
Symbol 187 Text	Uses:3	Used by:Timeline
Symbol 188 Text	Uses:3	Used by:Timeline
Symbol 189 Text	Uses:163	Used by:Timeline
Symbol 190 Text	Uses:3	Used by:Timeline
Symbol 191 Graphic	Used by:Timeline
Symbol 192 Text	Uses:3	Used by:Timeline
Symbol 193 Text	Uses:3	Used by:Timeline
Symbol 194 Graphic	Used by:Timeline
Symbol 195 Text	Uses:3	Used by:Timeline
Symbol 196 Graphic	Used by:Timeline
Symbol 197 Graphic	Used by:Timeline
Symbol 198 Text	Uses:3	Used by:Timeline
Symbol 199 Text	Uses:3	Used by:Timeline
Symbol 200 Text	Uses:3	Used by:Timeline
Symbol 201 Text	Uses:3	Used by:Timeline
Symbol 202 Graphic	Used by:Timeline
Symbol 203 Graphic	Used by:Timeline
Symbol 204 Text	Uses:3	Used by:Timeline
Symbol 205 Graphic	Used by:Timeline
Symbol 206 Text	Uses:3	Used by:Timeline
Symbol 207 Graphic	Used by:Timeline
Symbol 208 Text	Uses:3	Used by:Timeline
Symbol 209 Graphic	Used by:Timeline
Symbol 210 Text	Uses:3	Used by:Timeline
Symbol 211 Graphic	Used by:Timeline
Symbol 212 Text	Uses:3	Used by:Timeline
Symbol 213 Graphic	Used by:Timeline
Symbol 214 Graphic	Used by:Timeline
Symbol 215 Text	Uses:3	Used by:Timeline
Symbol 216 Text	Uses:3	Used by:Timeline
Symbol 217 Text	Uses:3	Used by:Timeline
Symbol 218 Graphic	Used by:219
Symbol 219 MovieClip	Uses:218	Used by:Timeline
Symbol 220 Text	Uses:3	Used by:Timeline
Symbol 221 Text	Uses:3	Used by:Timeline
Symbol 222 Text	Uses:79	Used by:Timeline
Symbol 223 Font	Used by:224
Symbol 224 Text	Uses:223	Used by:Timeline
Symbol 225 Font	Used by:226 228
Symbol 226 Text	Uses:225	Used by:Timeline
Symbol 227 Text	Uses:105	Used by:Timeline
Symbol 228 Text	Uses:225	Used by:Timeline
Symbol 229 Text	Uses:3	Used by:Timeline
Symbol 230 Graphic	Used by:Timeline
Symbol 231 Graphic	Used by:Timeline
Symbol 232 Text	Uses:3	Used by:Timeline
Symbol 233 Graphic	Used by:Timeline
Symbol 234 Text	Uses:3	Used by:Timeline
Symbol 235 Bitmap	Used by:236 239 241 281 283
Symbol 236 Graphic	Uses:235	Used by:237
Symbol 237 MovieClip	Uses:236	Used by:Timeline
Symbol 238 Graphic	Used by:Timeline
Symbol 239 Graphic	Uses:235	Used by:240
Symbol 240 MovieClip	Uses:239	Used by:Timeline
Symbol 241 Graphic	Uses:235	Used by:242
Symbol 242 MovieClip	Uses:241	Used by:Timeline
Symbol 243 Text	Uses:3	Used by:Timeline
Symbol 244 Text	Uses:3	Used by:Timeline
Symbol 245 Text	Uses:3	Used by:Timeline
Symbol 246 Graphic	Used by:Timeline
Symbol 247 Graphic	Used by:Timeline
Symbol 248 Graphic	Used by:Timeline
Symbol 249 Text	Uses:3	Used by:Timeline
Symbol 250 Graphic	Used by:251
Symbol 251 MovieClip	Uses:250	Used by:Timeline
Symbol 252 Text	Uses:3	Used by:Timeline
Symbol 253 Graphic	Used by:Timeline
Symbol 254 Text	Uses:3	Used by:Timeline
Symbol 255 Graphic	Used by:Timeline
Symbol 256 Text	Uses:3	Used by:Timeline
Symbol 257 Text	Uses:3	Used by:Timeline
Symbol 258 Text	Uses:3	Used by:Timeline
Symbol 259 Text	Uses:3	Used by:Timeline
Symbol 260 Text	Uses:3	Used by:Timeline
Symbol 261 Text	Uses:3	Used by:Timeline
Symbol 262 Text	Uses:3	Used by:Timeline
Symbol 263 Text	Uses:3	Used by:Timeline
Symbol 264 Text	Uses:3	Used by:Timeline
Symbol 265 Text	Uses:3	Used by:Timeline
Symbol 266 Text	Uses:3	Used by:Timeline
Symbol 267 Text	Uses:3	Used by:Timeline
Symbol 268 Text	Uses:3	Used by:Timeline
Symbol 269 Text	Uses:3	Used by:Timeline
Symbol 270 Font	Used by:271
Symbol 271 Text	Uses:270	Used by:Timeline
Symbol 272 Text	Uses:3	Used by:Timeline
Symbol 273 Graphic	Used by:Timeline
Symbol 274 Text	Uses:3	Used by:Timeline
Symbol 275 Graphic	Used by:Timeline
Symbol 276 Text	Uses:3	Used by:Timeline
Symbol 277 Graphic	Used by:Timeline
Symbol 278 Text	Uses:3	Used by:Timeline
Symbol 279 Text	Uses:3	Used by:Timeline
Symbol 280 Text	Uses:3	Used by:Timeline
Symbol 281 Graphic	Uses:235	Used by:282
Symbol 282 MovieClip	Uses:281	Used by:Timeline
Symbol 283 Graphic	Uses:235	Used by:Timeline
Symbol 284 Text	Uses:3	Used by:Timeline
Symbol 285 Text	Uses:3	Used by:Timeline
Symbol 286 Graphic	Used by:Timeline
Symbol 287 Text	Uses:3	Used by:Timeline
Symbol 288 Text	Uses:3	Used by:Timeline
Symbol 289 Bitmap	Used by:290
Symbol 290 Graphic	Uses:289	Used by:Timeline
Symbol 291 Bitmap	Used by:294
Symbol 292 Bitmap	Used by:294
Symbol 293 Bitmap	Used by:294
Symbol 294 Graphic	Uses:291 292 293	Used by:Timeline
Symbol 295 Text	Uses:3	Used by:Timeline
Symbol 296 Text	Uses:3	Used by:Timeline
Symbol 297 Text	Uses:3	Used by:Timeline
Symbol 298 Text	Uses:3	Used by:Timeline
Symbol 299 Text	Uses:3	Used by:Timeline

Instance Names

"loader"	Frame 1	Symbol 2 MovieClip
"prev"	Frame 2	Symbol 12 Button
"next"	Frame 2	Symbol 15 Button
"targpos"	Frame 38	Symbol 1 MovieClip
"targpos"	Frame 46	Symbol 1 MovieClip
"targpos"	Frame 50	Symbol 1 MovieClip
"targpos"	Frame 54	Symbol 1 MovieClip
"targpos"	Frame 68	Symbol 1 MovieClip
"targpos"	Frame 73	Symbol 1 MovieClip
"targpos"	Frame 90	Symbol 1 MovieClip
"shell"	Symbol 2 MovieClip Frame 1	Symbol 1 MovieClip

Dynamic Text Variables

pagedisplay

Symbol 16 EditableText

"2"