moving and rotating objects along a sine wave

There are a couple of problems i'm having with this - the first is how to work out how to find where the tip of each sine curve is (ie the frequency) and the second is to work out how to rotate each object so that it slides sideways along the sine wave

(note file is 800 x 600)

here's my code: CarouselTest.as:

package  
{
    import com.greensock.easing.Sine;
    import com.greensock.TweenMax;
    import com.components.CarouselItem;
    import com.theflashblog.fp10.SimpleZSorter;
    import flash.display.Sprite;
    import flash.events.Event;
    import uk.co.thereceptacle.utils.Trig;

    public class CarouselTest extends Sprite 
    {
        public static const SPACING : int = 20;
        public static const XSPACING: int = SPACING * 5;
        public static const SPEED   : Number = .05;
        public static const XSPEED  : Number = 800 / 360 * 2;
        public static const RADIUS  : int = 400;

        private var _items:Array;
        private var _container:Sprite;
        private var _movePerItem:Number;
        private var _noOfItems:int;

        public function CarouselTest() 
        {
            _items = new Array();
            _noOfItems = 200;
            _movePerItem = 360 / _noOfItems; // my attempt at finding how much each item must move in order to bring it to the front

            _container = new Sprite();
            _container.x = 400;
            _container.y = 300;
            _container.z = 200;
            addChild(_container);

            var item:CarouselItem = new CarouselItem();
            for (var i:int = 0; i < _noOfItems; i++)
            {
                item = new CarouselItem();
                item.radius = RADIUS;
                item.angle = (i * SPACING) % 360;
                item.x = i * XSPACING - 300;
                item.speed = SPEED;
                _container.addChild(item);
                _items.push(item);
            }

            moveItems(-1 * _movePerItem);
        }

        private function moveItems(direction:int):void
        {
            TweenMax.allTo(_items, 5, { angle:direction.toString(), x:(direction * XSPACING).toString(), ease:Sine.easeInOut } );
            TweenMax.to(this, 5, { onUpdate:SimpleZSorter.sortClips, onUpdateParams:[_container] } );
        }
    }
}

CarouselItem.as

package com.components 
{
    import flash.display.Sprite;
    import flash.text.TextField;
    import uk.co.thereceptacle.components.HTMLTextField;
    import uk.co.thereceptacle.utils.Trig;

    public class CarouselItem extends Sprite
    {
        private var _angle  : Number;
        private var _prevX  : Number;
        private var _prevZ  : Number;

        public var speed    : int;
        public var radius   : Number;

        public function CarouselItem() 
        {
            graphics.beginFill(0x99ff00);
            graphics.lineStyle(1);
            graphics.drawRect( -100, -150, 200, 300);

            var tf:TextField = new HTMLTextField();
            tf.embedFonts = false;
            tf.wordWrap = false;
            tf.htmlText = "<p>THIS IS A TEST</p>";
            tf.x = -100;
    开发者_运维技巧        tf.y = -tf.textHeight / 2;
            addChild(tf);
        }

        public function get angle():Number { return _angle; }
        public function set angle(value:Number):void 
        {
            _angle = value;

            z = Math.sin(angle) * radius;

            var deltaX:Number = x - _prevX;
            var deltaZ:Number = z - _prevZ;
            var rotate:Number = Trig.radiansToDegrees(Math.atan2(deltaZ, deltaX));
            rotationY = rotate; <strike>// this is getting close but always rotates the item away from the center and i need it to rotate towards the center on the positive side of the sine wave</strike>
// edit: i've updated this as it's much closer but still flaky - it feels like i haven't done it right

        }

        override public function set x(value:Number):void 
        {
            _prevX = x;
            super.x = value;
        }

        override public function set z(value:Number):void 
        {
            _prevZ = z;
            super.z = value;
        }
    }
}

hope you can help obie

---

I assume you want to animate something like a skateboard on a rolling hill (or boat on seas, or something with similar motion).

All of the trig/calculus you need to know for this problem: The line sitting on a curve in the way you want is the tangent line. It is described by the derivative of the curve. The derivative of the sine curve is the cosine. Calculus magic: if your curve is a*sin(b*x), the tangent is a*b*cos(b*x). That gives you (rise/run). If you want this expressed as an angle, you will want the atan (or atan2) of that. Note, you will need to be consistent with your angle units. Most likely atan gives you radians and you want degrees.