Unity game Development Math and Physics 4 (adding gravity to Object motion)

Adding gravity to the motion of an object

Implementation NOTE:

• Using the series overlay algorithm
• Y + = VY; The acceleration on the position
• VY + = GR;//acceleration on SPEED
• GR is the gravitational acceleration, the acceleration unit used in the computer is a special dot/f^2 ( pixel/square frame ) instead of 9.8 m/s^2 (M/s)
• Differential is an operation, is a differential coefficient of operation, and the differential coefficient refers to the function about a value of the rate of change , this concept in game development is often used to examine the speed of a function change; F (x) about the rate of change of x, the basic differential formula
• D/DX (x) = 1
• D/DX (x^2) = 2x
• D/DX (x^3) = 3x
• D/DX (x^n) = nx^ (n-1)
• D/dx (sin x) = cos x
• D/DX (cos x) =-sin x
• The derivative of a synthetic function can be regarded as "the differential of an equation that contains another layer of function, which can be converted into a derivative of the outer layer function multiplied by the differentiation of the inner layer function"
• Progression is the result of adding up each item of a sequence.
• The integral and the series have similar parts, from the formal point of view is the differential inverse
• Parabolic motion program with integral production
• x = VX * t;

• y = (0.5f * GR * t * t) + (VY * t) + 200.0f;

• The following code uses integrals to make parabolic

usingUnityengine;usingSystem.Collections;//Adding gravity to the motion of the object Public classParabolicmotiontest:monobehaviour {//X position of Object    floatPosX =0;//Y position of Object    floatPosY =0;//speed of the object in the x direction    floatSpeedx =0;//speed of the object in the y direction    floatSpeedY =-8;//The top right pixel of the screen in world space coordinatesVector3 Screenrighttoppos;//The left lower pixel of the screen in world space coordinatesVector3 Screenleftbottompos;half width of//box    floatBoxhalfwidth;//Run time    floatRunTime;//Gravitational acceleration    Const floatGR =0.4F//Where the object was bornVector2 Bornpos;voidStart () {//Convert the pixel on the right of the screen to the coordinates of world spaceScreenrighttoppos = Camera.main.ScreenToWorldPoint (NewVector3 (Screen.width, Screen.height,0));//Convert the pixel at the bottom right of the screen to the coordinates of world spaceScreenleftbottompos = Camera.main.ScreenToWorldPoint (NewVector3 (0,0,0));//box half width, because box is squareBoxhalfwidth = transform.localscale.x *0.5F//Birth location upper left cornerBornpos =NewVector2 (screenleftbottompos.x + boxhalfwidth, screenrighttoppos.y-boxhalfwidth);//Initial position screen upper left cornerTransform.localposition =NewVector3 (Bornpos.x, Bornpos.y,0); }voidUpdate () {//Detect, if the object is out of the interface, let it go back to the Bornpos point        if(posx-boxhalfwidth >= screenrighttoppos.x | | PosX + boxhalfwidth <= screenleftbottompos.x | | Posy-boxhalfwidth >= Screenrighttoppos.y | | PosY + boxhalfwidth <= screenleftbottompos.y) {//upper left corner of the screenPosX = bornpos.x; PosY = Bornpos.y;//Run time 0RunTime =0; }//x direction of displacement to a value per frame of timePosX = Speedx * runTime;//y direction of displacement to a value per frame of timePosY = (0.5F * GR * Runtime * Runtime) + (SpeedY * runtime) + Bornpos.y;//Time change valueRunTime + = Time.deltatime;//Set the position of the frameTransform.localposition =NewVector3 (PosX, PosY,0); }}

Unity game Development Math and Physics 4 (adding gravity to Object motion)