Eng:Simulating Gravity

Simulating Gravity, or at least the effect of gravity in Scratch can be difficult, but due to trigonometric blocks in Scratch, it is possible.

Creating Gravity Using Trigonometry
This section is designed to teach you how to simulate gravity's pull on an object around a center-point. This is similar to how the gravity of a star affects the motion of a planet.

The script below is based on a simple trigonometric identity which states that sin2x + cos2y = 1.

Below are the scripts you will need to put into the object that you want to rotate:

when flag clicked set [Distance v] to [100] set [Rotation v] to [0] forever repeat (360) go to x: ((([sin v] of (Rotation)) * (Distance)) + ([x position v] of [Sprite2 v])) y: ((([cos v] of (Rotation)) * (distance)) + ([y position v] of [Sprite2 v])) point in direction (([direction v] of [Sprite2 v]) + (90)) if <[359] < (Rotation)> then set [Rotation v] to [0] end if <[-359] > (Rotation)> then set [Rotation v] to [0] end if > then change [Distance v] by (-1.5) end end

If you want the person playing the game to control the rotation you can use this script:

when flag clicked forever if  then change [Rotation v] by (2) switch to costume [costume3 v] end

when flag clicked forever if  then repeat (10) change [Distance v] by (5) end wait until  end

when flag clicked forever if  then change [Rotation v] by (-2) switch to costume [costume4 v] end

For the "Planet" or other object that is being rotated about you will want to use this script:

when flag clicked forever point towards [planet v]

Make sure you set the "Planet" or other object's rotation to "do not rotate".

Using trigonometry is a smooth and effective way for more experienced Scratchers to simulate gravity. With some more advanced scripts you can even rotate about non-circular objects.

An example of trigonometric gravity can be seen here.

Creating Gravity Using Rotation
Another method of simulating gravity is to change the center of a sprite so when you rotate it, it appears to be pulled by gravity. This method is much more simple, but far more difficult to achieve.
 * 1) Change the sprite's center to the center of the planet. Paint Editor With Sprite Center in Center.png
 * 2) Repeat Step 1 for every single sprite of that character.
 * 3) Write scripts for each sprite for every different situation:

when flag clicked show go to x: (0) y: (0) point in direction (0 v) forever if  or < or >>> then if  then switch to costume [costume1 v] end end end

when flag clicked forever wait until  play sound [jump v] repeat (20) switch to costume [costume4 v] move (1.5) steps end repeat (10) switch to costume [costume4 v] move (1) steps end repeat (10) switch to costume [costume4 v] move (-1) steps end repeat (10) switch to costume [costume4 v] move (-1.5) steps end switch to costume [costume1 v] go to x: (0) y: (0) end

when flag clicked forever if < and >> then turn cw (5) degrees switch to costume [costume2 v] wait (0.05) secs turn cw (5) degrees switch to costume [costume3 v] wait (0.05) secs end if < and > then turn cw (5) degrees switch to costume [costume4 v] wait (0.05) secs turn cw (5) degrees switch to costume [costume4 v] wait (0.05) secs end end

when flag clicked forever if < and >> then turn cw (-5) degrees switch to costume [costume5 v] wait (0.05) secs turn cw (-5) degrees switch to costume [costume 6 v] wait (0.05) secs end if <<key [left arrow v] pressed?> and <key [up arrow v] pressed?>> then turn cw (-5) degrees switch to costume [costume4 v] wait (0.05) secs turn cw (-5) degrees switch to costume [costume4 v] wait (0.05) secs end end

One example of rotational gravity can be seen here.

Creating Gravity Using Physics
One advanced technique for simulating gravity involves Newton's law of universal Gravity:



Variables and Lists
From this equation and Newton's 2nd Law of Motion (which states that F = ma) we can solve for the change in velocity of an object as: a = (Gm2)/(r2)

This describes the acceleration of one object due to the gravity of another (with mass = m2)

In the equation above, three variables can be seen to be needed:


 * G (Newton's universal law of gravity)
 * m2(mass of the other object)
 * r (the distance the objects are from each other)

G is a universal constant and can often lead to masses and distances that seem very awkward or unintuitive. To simplify the equation and allow you to use easier/friendlier numbers, we can actually ignore G. When you choose your relative masses you will be factoring it in. If the project involves very large (e.g. Moon-sized) masses and large (e.g. low-orbital level) distances, use 6.67*10-11 for G.

Along the mass of object two and its distance, the speed of the moving object (object one) will need to be stored:


 * X Velocity
 * Y Velocity

Also, to turn the acceleration into its x and y components, a ratio will be used (this is based on the idea that the x and y forces form a right triangle similar to that formed by the objects themselves)


 * Ratio

Finally, a variable will be used to iterate through every mass and every object's x and y position:


 * I

Those masses will be stored in a list:


 * Masses

As well as the x and y positions:


 * X Positions
 * Y Positions

Scripting
To begin, a custom block is needed that will iterate through every object in the project:

define Check Objects//make sure this runs without screen refresh! set [I v] to (1)//the beginning of the list repeat (length of [Masses v])//each object takes up two items in the list . . .//this is where the calculations will go   change [I v] by (1)//moving onto the next object end

To note, the custom block needs to run without a screen refresh. After the custom block is created, the distance between the sprite and an object needs to be computed:

define Check Objects set [I v] to (1)//the beginning of the list repeat (length of [Masses v]) set [Dist. v] to ([sqrt v] of ((((item (I) of [X Positions v]) - (X Position))*((item (I) of [X Positions v]) - (X Position))) + (((item (i) of [Y Positions v]) - (Y Position))*((item (i) of [Y Positions v]) - (Y Position))))   change [I v] by (1) end

Next, the overall acceleration is needed:

define Check Objects set [I v] to (1)//the beginning of the list repeat (length of [Masses v]) set [Dist. v] to ([sqrt v] of ((((item (I) of [X Positions v]) - (X Position))*((item (I) of [X Positions v]) - (X Position))) + (((item (i) of [Y Positions v]) - (Y Position))*((item (i) of [Y Positions v]) - (Y Position)))) set [Acceleration v] to ((item (i) of [Masses v]) / ((Dist.) * (Dist.)))// equation we found above change [I v] by (1) end

Next, the force is needed to turn into its x and y components. To achieve this, the force will be compared to the distance, and that ratio, when compared to the horizontal/vertical distance between the sprite and an object, will achieve just that:

define Check Objects set [I v] to (1)//the beginning of the list repeat (length of [Masses v]) set [Dist. v] to ([sqrt v] of ((((item (I) of [X Positions v]) - (X Position))*((item (I) of [X Positions v]) - (X Position))) + (((item (i) of [Y Positions v]) - (Y Position))*((item (i) of [Y Positions v]) - (Y Position)))) set [Acceleration v] to ((item (i) of [Masses v]) / ((Dist.) * (Dist.)))//equation we found above   set [Ratio v] to ((Acceleration) / (Dist.))    change [X Velocity v] by ((Ratio) * ((item (I) of [X Positions v]) - (X Position)))//x component of the force vector    change [Y Velocity v] by ((Ratio) * ((item (i) of [Y Positions v]) - (Y Position)))//y component of force vector    change [I v] by (1) end

The script is now done, though the variables X Velocity and Y Velocity need to have some use:

when gf clicked set [X Velocity v] to (0) set [Y Velocity v] to (0) forever Check Objects change x by (X Velocity)//applying the velocities change y by (Y Velocity)

define Check Objects . . .//refer above for the coding

Final Product
Once the steps above have been followed, this should be the final coding:

define Check Objects set [I v] to (1)//the beginning of the list repeat (length of [Masses v]) set [Dist. v] to ([sqrt v] of ((((item (I) of [X Positions v]) - (X Position))*((item (I) of [X Positions v]) - (X Position))) + (((item (i) of [Y Positions v]) - (Y Position))*((item (i) of [Y Positions v]) - (Y Position)))) set [Acceleration v] to ((item (i) of [Masses v]) / ((Dist.) * (Dist.)))//equation we found above   set [Ratio v] to ((Acceleration) / (Dist.))    change [X Velocity v] by ((Ratio) * ((item (I) of [X Positions v]) - (X Position)))//x component of the force vector    change [Y Velocity v] by ((Ratio) * ((item (i) of [Y Positions v]) - (Y Position)))//y component of force vector    change [I v] by (1) end

when gf clicked set [X Velocity v] to (0) set [Y Velocity v] to (0) forever Check Objects change x by (X Velocity)//applying the velocities change y by (Y Velocity)

Simulating Gravity in Scrollers
Gravity can be replicated on Scratch to be used in Scrollers and other project where an object is forced downward. Listed below are several methods that you can use.

Velocity Method
The Velocity Method is a great method for creating gravity and is highly effective and adaptable for multiple situations. Here is an example scriptplease note, this script will have the sprite inside the ground, rather than on top of it. This script will be placed into the Sprite that is being affected by gravity:

when flag clicked go to x: (0) y: (0) forever change y by (Y Velocity) set [Y Velocity v] to ((Y Velocity) * (0.98)) when flag clicked forever if <not<touching [Ground v]?>> then change [Y Velocity v] by (-0.1) end when flag clicked forever if <touching [Ground v]?> then set [Y Velocity v] to [0] end wait until <not<touching [Ground v]?>>

Click here to see an example.

Direct Movement Method
Direct movement is more simple than the Velocity Method, but far less efficient at what it does. Not only does the jump look unrealistic, but it is far less practical in almost all situations. Nonetheless, the script works and is a good starting point for beginners:

when flag clicked forever if <not <touching [Ground v]?>> then change y by (-1) end end

when flag clicked forever if <key [up arrow v] pressed?> then repeat (10) change y by (10) end end wait until <touching [Ground v]?>

Examples

 * Direct Movement Example by dazman_test
 * Platformer v0.2 by Backlong
 * First Project: Blob Advanced by Blobzer22
 * Cross Sections by poose