Difference between revisions of "User:Etho/Physics Engine"

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m (Physics Engine (Worms Armageddon) moved to Physics Engine: Not really W:A-specific)
m (The wiki doesn't support single line breaks, so I've made this easier to read by using lists and codes.)
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* [[Worm Walking]]
 
* [[Worm Walking]]
  
−
x = x0 + vx0*t + w*t*(t+1)/2
+
  x = x0 + vx0*t + w*t*(t+1)/2
−
y = y0 + vy0*t + g*t*(t+1)/2
+
  y = y0 + vy0*t + g*t*(t+1)/2
−
vx = vx0 + w*t
+
  vx = vx0 + w*t
−
vy = vy0 + g*t
+
  vy = vy0 + g*t
  
 
Where
 
Where
−
t = time in ticks, a.k.a. frames (50ths of a second)
+
* t = time in ticks, a.k.a. frames (50ths of a second)
−
x = horizontal position (pixels)
+
* x = horizontal position (pixels)
−
y = vertical position (pixels)
+
* y = vertical position (pixels)
−
x0 = initial horizontal position (pixels)
+
* x0 = initial horizontal position (pixels)
−
y0 = initial vertical position (pixels)
+
* y0 = initial vertical position (pixels)
−
vx = horizontal speed (pixels per tick)
+
* vx = horizontal speed (pixels per tick)
−
vy = vertical speed (pixels per tick)
+
* vy = vertical speed (pixels per tick)
−
vx0 = initial horizontal speed (pixels per tick)
+
* vx0 = initial horizontal speed (pixels per tick)
−
vy0 = initial vertical speed (pixels per tick)
+
* vy0 = initial vertical speed (pixels per tick)
−
w = wind (pixels per tick per tick)
+
* w = wind (pixels per tick per tick)
−
g = gravity (pixels per tick per tick)
+
* g = gravity (pixels per tick per tick)
  
 
And g=0.24. For a worm of course, w=0.
 
And g=0.24. For a worm of course, w=0.
  
 
ProvX = ((iPosX(X)) + (VeloX(X) / 1000) * Tick(X) + ((WindSpeed / 1000) * (Wind(X) / 100)) * Tick(X) * (Tick(X) + 1) / 2)
 
ProvX = ((iPosX(X)) + (VeloX(X) / 1000) * Tick(X) + ((WindSpeed / 1000) * (Wind(X) / 100)) * Tick(X) * (Tick(X) + 1) / 2)
 +
 
ProvY = ((iPosY(X)) + (VeloY(X) / 1000) * Tick(X) + (Gravity / 1000) * Tick(X) * (Tick(X) + 1) / 2)
 
ProvY = ((iPosY(X)) + (VeloY(X) / 1000) * Tick(X) + (Gravity / 1000) * Tick(X) * (Tick(X) + 1) / 2)
  
−
Add gravity to vertical speed.  
+
* Add gravity to vertical speed.  
−
Add wind to horizontal speed.  
+
* Add wind to horizontal speed.  
−
Add horizontal speed to provisional X coordinate.  
+
* Add horizontal speed to provisional X coordinate.  
−
Add vertical speed to provisional Y coordinate.  
+
* Add vertical speed to provisional Y coordinate.  
−
Check for collisions between last coordinates and provisional coordinates; if there's a collision, handle it. Otherwise, move to provisional coordinates.  
+
* Check for collisions between last coordinates and provisional coordinates; if there's a collision, handle it. Otherwise, move to provisional coordinates.  
−
Start again for the next frame.
+
* Start again for the next frame.
  
 
* FPS = 50/sec
 
* FPS = 50/sec
Line 42: Line 43:
 
* forward jump  
 
* forward jump  
 
* max speed = 32 pixels/frame
 
* max speed = 32 pixels/frame
 +
 
Screen Width = 6012
 
Screen Width = 6012
 +
 
2046 - 1920 - 2046
 
2046 - 1920 - 2046
  
 +
Vertical Distance of a 90 degree bazooka = 1200 pixels (aprox); velocity = -24.12
  
−
Verticle Distance of a 90 degree bazooka = 1200 pixels (aprox); velocity = -24.12
 
 
Wormmask = SpriteX + 25, SpriteY + 21
 
Wormmask = SpriteX + 25, SpriteY + 21
  
−
Forward Jump = 45 - 16 = 29; velocity = sin(60) * 4.5
+
  Forward Jump = 45 - 16 = 29; velocity = sin(60) * 4.5
−
At 0/0. horizontal change = 70 pixels, = +/-2.25
+
  At 0/0. horizontal change = 70 pixels, = +/-2.25
−
Backwards Jump = 54 - 16 = 38; velocity = sin(80) * 4.5
+
  Backwards Jump = 54 - 16 = 38; velocity = sin(80) * 4.5
−
At 0/0. horizontal change = 28 pixels, = +/-0.7814167995
+
  At 0/0. horizontal change = 28 pixels, = +/-0.7814167995
−
Straight Jump = 55 - 16 = 39; velocity => -4.446... < 4.502...
+
  Straight Jump = 55 - 16 = 39; velocity => -4.446... < 4.502...
−
At 0/0. horizontal change = 0 pixels, = 0
+
  At 0/0. horizontal change = 0 pixels, = 0
−
Backflip Jump = 87 - 16 = 71; velocity => -5.9583... < 6.000 sin(85)*6?
+
  Backflip Jump = 87 - 16 = 71; velocity => -5.9583... < 6.000 sin(85)*6?
−
At 0/0, horizontal change = 21 pixels; = +/- 0.434
+
  At 0/0, horizontal change = 21 pixels; = +/- 0.434
  
 
X = 0.42413
 
X = 0.42413
 +
 
Y = -5.98799
 
Y = -5.98799
 +
 
it starts with 90-3.6 degrees (86.4 degrees) with magnitude 4.5 then multiplies X by 3/2 and Y by 4/3
 
it starts with 90-3.6 degrees (86.4 degrees) with magnitude 4.5 then multiplies X by 3/2 and Y by 4/3
  
 
Walking Frame Rate = 50 / 3 (3 cycles per second)
 
Walking Frame Rate = 50 / 3 (3 cycles per second)
  
−
+0.50
+
  +0.50
−
no motion
+
  no motion
−
+0.50
+
  +0.50
−
+0.50
+
  +0.50
−
+0.50
+
  +0.50
−
+0.50
+
  +0.50
−
+1.50
+
  +1.50
−
+1.75
+
  +1.75
−
+1.50
+
  +1.50
−
+1.25
+
  +1.25
−
skip here and avoid the slower phase:
+
  skip here and avoid the slower phase:
−
+0.25
+
  +0.25
−
no motion
+
  no motion
−
+0.25
+
  +0.25
−
+0.25
+
  +0.25
−
+0.25
+
  +0.25
−
no motion
+
  no motion
−
no motion
+
  no motion
−
no motion
+
  no motion
 
repeat - but not quite; "no motion" frames shift and the period of true repetition is 50 frames travelling 27 pixels
 
repeat - but not quite; "no motion" frames shift and the period of true repetition is 50 frames travelling 27 pixels
  
 
The optimum skipwalk cycle is actually 4.545 per second, because it has a period of 11 frames = 11/50 second.
 
The optimum skipwalk cycle is actually 4.545 per second, because it has a period of 11 frames = 11/50 second.
 +
 
Fall Damage = 158 pixels - 16 pixels = 142 pixels
 
Fall Damage = 158 pixels - 16 pixels = 142 pixels
  
 
worm rect = 16x9
 
worm rect = 16x9
−
0XXXXXXX0
+
  0XXXXXXX0
−
0XXXXXXX0
+
  0XXXXXXX0
−
0XXXXXXX0
+
  0XXXXXXX0
−
0XXXXXXX0
+
  0XXXXXXX0
−
XXXXXXXXX
+
  XXXXXXXXX
−
XXXXXXXXX
+
  XXXXXXXXX
−
XXXXXXXXX
+
  XXXXXXXXX
−
XXXXXXXXX
+
  XXXXXXXXX
−
XXXXXXXXX
+
  XXXXXXXXX
−
XXXXXXXXX
+
  XXXXXXXXX
−
0XXXXXXX0
+
  0XXXXXXX0
−
0XXXXXXX0
+
  0XXXXXXX0
−
0XXXXXXX0
+
  0XXXXXXX0
−
00XXXXX00
+
  00XXXXX00
−
00XXXXX00
+
  00XXXXX00
−
00XXXXX00
+
  00XXXXX00
−
 
+
−
 
+
−
sorry for the mess... I was just listing random thoughts (clean it up please)
+

Revision as of 16:00, 2 May 2007

 x = x0 + vx0*t + w*t*(t+1)/2
 y = y0 + vy0*t + g*t*(t+1)/2
 vx = vx0 + w*t
 vy = vy0 + g*t

Where

  • t = time in ticks, a.k.a. frames (50ths of a second)
  • x = horizontal position (pixels)
  • y = vertical position (pixels)
  • x0 = initial horizontal position (pixels)
  • y0 = initial vertical position (pixels)
  • vx = horizontal speed (pixels per tick)
  • vy = vertical speed (pixels per tick)
  • vx0 = initial horizontal speed (pixels per tick)
  • vy0 = initial vertical speed (pixels per tick)
  • w = wind (pixels per tick per tick)
  • g = gravity (pixels per tick per tick)

And g=0.24. For a worm of course, w=0.

ProvX = ((iPosX(X)) + (VeloX(X) / 1000) * Tick(X) + ((WindSpeed / 1000) * (Wind(X) / 100)) * Tick(X) * (Tick(X) + 1) / 2)

ProvY = ((iPosY(X)) + (VeloY(X) / 1000) * Tick(X) + (Gravity / 1000) * Tick(X) * (Tick(X) + 1) / 2)

  • Add gravity to vertical speed.
  • Add wind to horizontal speed.
  • Add horizontal speed to provisional X coordinate.
  • Add vertical speed to provisional Y coordinate.
  • Check for collisions between last coordinates and provisional coordinates; if there's a collision, handle it. Otherwise, move to provisional coordinates.
  • Start again for the next frame.
  • FPS = 50/sec
  • standard gravity = 0.24
  • standard friction = 0.96
  • low gravity friction = 0.99

friction multiplies a number every frame until the number becomes small enough

  • max pixel climb walking = 14 pixels
  • max pixel decline walking = 13 pixels
  • max pixel climb sliding = 1 pixel
  • color key = 0
  • forward jump
  • max speed = 32 pixels/frame

Screen Width = 6012

2046 - 1920 - 2046

Vertical Distance of a 90 degree bazooka = 1200 pixels (aprox); velocity = -24.12

Wormmask = SpriteX + 25, SpriteY + 21 

 Forward Jump = 45 - 16 = 29; velocity = sin(60) * 4.5
 At 0/0. horizontal change = 70 pixels, = +/-2.25
 Backwards Jump = 54 - 16 = 38; velocity = sin(80) * 4.5
 At 0/0. horizontal change = 28 pixels, = +/-0.7814167995
 Straight Jump = 55 - 16 = 39; velocity => -4.446... < 4.502...
 At 0/0. horizontal change = 0 pixels, = 0
 Backflip Jump = 87 - 16 = 71; velocity => -5.9583... < 6.000 sin(85)*6?
 At 0/0, horizontal change = 21 pixels; = +/- 0.434

X = 0.42413

Y = -5.98799

it starts with 90-3.6 degrees (86.4 degrees) with magnitude 4.5 then multiplies X by 3/2 and Y by 4/3

Walking Frame Rate = 50 / 3 (3 cycles per second) 

 +0.50
 no motion
 +0.50
 +0.50
 +0.50
 +0.50
 +1.50
 +1.75
 +1.50
 +1.25
 skip here and avoid the slower phase:
 +0.25
 no motion
 +0.25
 +0.25
 +0.25
 no motion
 no motion
 no motion

repeat - but not quite; "no motion" frames shift and the period of true repetition is 50 frames travelling 27 pixels

The optimum skipwalk cycle is actually 4.545 per second, because it has a period of 11 frames = 11/50 second.

Fall Damage = 158 pixels - 16 pixels = 142 pixels

worm rect = 16x9 

 0XXXXXXX0
 0XXXXXXX0
 0XXXXXXX0
 0XXXXXXX0
 XXXXXXXXX
 XXXXXXXXX
 XXXXXXXXX
 XXXXXXXXX
 XXXXXXXXX
 XXXXXXXXX
 0XXXXXXX0
 0XXXXXXX0
 0XXXXXXX0
 00XXXXX00
 00XXXXX00
 00XXXXX00
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