So I am currently making a Scrolling platformer boss fight and I set up the projectiles' physics engine like this (edited for relevancy):

define PlaneSlopeStart (InitialVel) (SpawnX) (SpawnY)
go to x:(SpawnX) y:(SpawnY)
point towards [character v]
move (InitialVel) steps
set [xvball v] to ((SpawnX) + ([x position v] of [Level v]))
set [yvball v] to ((SpawnY) + ([y position v] of [Level v]))
go to x:(SpawnX) y:(SpawnY)

and I need help finding the formula/steps to calculate the perfect trajectory for a projectile to hit a moving target or even a still target. I looked through multiple websites. The one that seems to have the answer is here, but I can't understand it fully.

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end

bump

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end

bumpity bump

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end

Hmm. You could make a custom block with run without screen refresh.
You could tweak the values of course (velocity might not be in steps and of course time is not accurate)

define calcTraj (vel) (timeSpan)
set [logX v] to (x position)
set [logY v] to (y position)
repeat (timeSpan)
move (vel) steps
end
set [xTraj v] to (x position)
set [yTraj v] to (y position)
go to x: (logX v) y: (logY v)

bSpyder wrote:

Hmm. You could make a custom block with run without screen refresh.
You could tweak the values of course (velocity might not be in steps and of course time is not accurate)

define calcTraj (vel) (timeSpan)
set [logX v] to (x position)
set [logY v] to (y position)
repeat (timeSpan)
move (vel) steps
end
set [xTraj v] to (x position)
set [yTraj v] to (y position)
go to x: (logX v) y: (logY v)

Tweaking this code to be compatible with scrolling platformers, the global variables would be a waste of space and local (procedure only) variables can replace it. The repeat timeSpan, move vel steps section doesn't make any sense to me.

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end

bump

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end

so say every tick the target moves.
And every tick the target moves its velocity.

Thats what timeSpan and vel means

bSpyder wrote:

so say every tick the target moves.
And every tick the target moves its velocity.

Thats what timeSpan and vel means

I see..

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end

bump

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end

This seems harder than I thought it would be. That website doesn't make clear how you go directly from the things you know (speed of projectile and horizontal distance) to the required angle.

But here's an approach (for calculating theta) that more or less works. Theta is the angle (above horizontal) you're looking for. S is the speed of the projectile. A is acceleration due to gravity. D is the horizontal distance away. This assumes everything is on the same horizontal level.

Theta = 90 - asin((-A/D)/(SxS))/2

Once you have calculated theta, the initial velocities will be vx = S x cos(theta) and vy = S x sin(theta). At each stage of a loop you change x position by VX, y position by VY, and VY by A.

I've tried this using S = 15, A = -1.

PutneyCat wrote:

This seems harder than I thought it would be. That website doesn't make clear how you go directly from the things you know (speed of projectile and horizontal distance) to the required angle.

But here's an approach (for calculating theta) that more or less works. Theta is the angle (above horizontal) you're looking for. S is the speed of the projectile. A is acceleration due to gravity. D is the horizontal distance away. This assumes everything is on the same horizontal level.

Theta = 90 - asin((-A/D)/(SxS))/2

Once you have calculated theta, the initial velocities will be vx = S x cos(theta) and vy = S x sin(theta). At each stage of a loop you change x position by VX, y position by VY, and VY by A.

I've tried this using S = 15, A = -1.

I'll try testing this out

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end

PutneyCat wrote:

S is the speed of the projectile.

What do you mean by the speed of the projectile? Is it the X velocity, Y velocity, or the speed defined by the move () steps block?

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end

Speed is just a measure of how fast your projectile can go (in any direction). Velocity is speed in a particular direction (vx = horizontal, vy = vertical).

(Think of a right angle triangle - speed is the length of the hypotenuse.)

Speed is what you would insert if you were using the “move x steps” block. But you probably won't want to use that block for something like this, because you'd have to repeatedly recalculate the angle of movement.

PutneyCat wrote:

Speed is just a measure of how fast your projectile can go (in any direction). Velocity is speed in a particular direction (vx = horizontal, vy = vertical).

(Think of a right angle triangle - speed is the length of the hypotenuse.)

Speed is what you would insert if you were using the “move x steps” block. But you probably won't want to use that block for something like this, because you'd have to repeatedly recalculate the angle of movement.

Okay

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end

PS:

For clarity, speed is the projectile's speed when first fired (it will change under the influence of gravity).

Also, looking again at the website, I think you can in fact just use the 10th equation (for stationary target). What confused me was that he seemed to start (in his right angle triangle illustration) by using x and y to refer to velocities. But in the set of 10 equations I think they refer to distances (in x and y directions). So you could try just implementing the 10th equation.

can you share the project? I need to figure out how the scrolling work for me to help u

ventoaurum wrote:

can you share the project? I need to figure out how the scrolling work for me to help u

Here it is https://scratch.mit.edu/projects/607938031

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end

PutneyCat wrote:

PS:

For clarity, speed is the projectile's speed when first fired (it will change under the influence of gravity).

Also, looking again at the website, I think you can in fact just use the 10th equation (for stationary target). What confused me was that he seemed to start (in his right angle triangle illustration) by using x and y to refer to velocities. But in the set of 10 equations I think they refer to distances (in x and y directions). So you could try just implementing the 10th equation.

I'll try…

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end

I'm sorry that I can't help you(I'm preparing for exam), but this link might help

PutneyCat wrote:

Theta = 90 - asin((-A/D)/(SxS))/2

Do you subtract 90, then divide by 2, or divide by 2, then subtract 90?

Visualisation:

(((90) - (...)) / (2))

((90) - ((...) / (2)))

if <<quick? :: #965B01> and <dog <lazy? ::  #965B01> :: #984723>> then
jump over x:( dog (x):: #984723) y:(dog(y):: #984723):: #112233
end