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ஒழுக்கின்மை (Paul Eres)
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« on: April 17, 2009, 04:27:42 PM » |
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How do you reverse left/right direction, given the current direction? That is, what's the formula for taking a direction and reversing it with respect to a vertical wall.
/ would become \
_ would stay _
| would stay |
this would also happen (if the bounce were against a horizontal wall): ^
I know, this is not phrased very clearly, but hopefully someone will be able to understand and suggest something.
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« Last Edit: April 20, 2009, 05:04:28 PM by Derek »
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andy wolff
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« Reply #1 on: April 17, 2009, 04:34:16 PM » |
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normally you would multiply the horizontal component by negative 1 for a vertical wall or the vertical component by -1 for a horizontal floor/ceiling, then recalculate the direction based on your components
also this would work
180-direction for a wall to the left
0-direction for a wall to the right
90-direction for a wall above
270-direction for a wall below
something like that
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raigan
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« Reply #3 on: April 18, 2009, 05:01:57 AM » |
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The general solution is to split your direction vector into two parts, one parallel to the wall and one perpendicular; to "bounce" you then just negate the perpendicular component and add it to the parallel component to get the new vector.
In the case of axis-aligned walls the decomposition is already done for you by the coordinate system, but in general you need to do a bit of geometry to decompose and re-assemble the direction vector.
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ஒழுக்கின்மை (Paul Eres)
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« Reply #4 on: April 18, 2009, 07:26:23 AM » |
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What is a direction vector? What is a vector in general?
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increpare
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« Reply #6 on: April 18, 2009, 07:33:02 AM » |
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What is a direction vector? instead of encoding directions as angles, use arrows that point in a particular direction (so north would be (0,1), north-west would be (-1,1)). It's traditional* to scale the arrows so that their length is 1 (so north-west would be written as (-1/root2,1/root2)). If you store them like this, flipping vertically just means negating the first coordinate. What is a vector in general? You probably don't want to know.[*and there're good reasons why] |
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« Last Edit: April 18, 2009, 07:41:50 AM by stephen lavelle »
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mirosurabu
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« Reply #7 on: April 18, 2009, 07:42:42 AM » |
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 How do you represent direction? Usually, directions are represented using vectors - x and y components of direction. If direction is represented using its x and y components [ x ][ y ] than negative vector (reverse direction) would be [ -x ][ -y ]. |
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andy wolff
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« Reply #8 on: April 18, 2009, 08:27:16 AM » |
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the x component of a vector is simply length*cos(angle) while the y component is length*sin(angle), and the angle of an x and y component is tan-1(y/x)
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Alex May
...is probably drunk right now.
Level 10
hen hao wan
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« Reply #9 on: April 18, 2009, 09:55:45 AM » |
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Actually defining a vector by angle and length is still fine and still a vector, it's just in a different coordinate system (polar as opposed to cartesian).
The maths for reversing a polar coordinate vector in that manner would be simple I think: just make the angle negative (and then if necessary add on 360 degrees to keep it 0 < angle < 360)
(for reflection against other angles (where the angle in the above example is zero) I expect you'd do something like angle = -(angle - wall angle) off the top of my head)
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Movius
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« Reply #10 on: April 18, 2009, 10:05:28 AM » |
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(for reflection against other angles (where the angle in the above example is zero) I expect you'd do something like angle = -(angle - wall angle) off the top of my head)
newAngle = wallAngle - (OldAngle - wallAngle) = 2*wallAngle - oldAngle otherwise correct to my extremely-tired brain. |
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moi
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« Reply #11 on: April 18, 2009, 10:08:25 AM » |
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Think of vector as coordinates (x,y). Can be 3D (x,y,z)
Other things that are useful to know:
-pythagorus theorem
-relation of sinus and cosinus to an angle
That's all.
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subsystems subsystems subsystems
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JLJac
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« Reply #12 on: April 18, 2009, 11:08:42 AM » |
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You define your speed vector as a point, containing x and y floats.
When hitting a vertical surface the x-component of the speed vector is flipped (multiplyed with -1) and the same goes for the y-component when hitting a horizontal surface.
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Zaphos
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« Reply #13 on: April 18, 2009, 11:52:23 AM » |
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(for reflection against other angles (where the angle in the above example is zero) I expect you'd do something like angle = -(angle - wall angle) off the top of my head)
newAngle = wallAngle - (OldAngle - wallAngle) = 2*wallAngle - oldAngle otherwise correct to my extremely-tired brain. I might call that wallNormal instead of wallAngle, in that it's 90 degrees off from the direction the wall is going ... |
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Movius
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« Reply #14 on: April 19, 2009, 04:09:19 AM » |
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It's worth noting that you may not even need "vector maths" (beyond storing position and velocity as (x,y) pairs,) in many situations. any elastic collisions involving walls that are vertical, horizontal or at any 45 degree angle can be calculated using only existing x and y velocity values and the negative sign. (for reflection against other angles (where the angle in the above example is zero) I expect you'd do something like angle = -(angle - wall angle) off the top of my head)
newAngle = wallAngle - (OldAngle - wallAngle) = 2*wallAngle - oldAngle otherwise correct to my extremely-tired brain. I might call that wallNormal instead of wallAngle, in that it's 90 degrees off from the direction the wall is going ... what he said |
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