function toRad(deg){return deg*(Math.PI/180);}
function toDeg(rad){return rad*(180/Math.PI);}
function getLeftTiltAngle(ev){
    // r = rotz(alpha)*rotx(beta)*roty(gamma)*rotz(-screen.orientation.angle)*colvec[1,0,0]
    // tilt = sin^-1(r.z)
    var b = toRad(ev.beta);
    var c = toRad(ev.gamma);
    var d = toRad(-screen.orientation.angle);
    var rz = Math.sin(b)*Math.sin(d)-Math.cos(b)*Math.sin(c)*Math.cos(d);
    return toDeg(Math.asin(rz));
}

function getLeftTiltAngleFromMotionEvent(motionEvent){
  var gravityX = motionEvent.acceleration.x - motionEvent.accelerationIncludingGravity.x;
  var gravityY = motionEvent.acceleration.y - motionEvent.accelerationIncludingGravity.y;
  var gravityZ = motionEvent.acceleration.z - motionEvent.accelerationIncludingGravity.z;
  var screenAngleRev = toRad(-screen.orientation.angle);
  var rightX = Math.cos(screenAngleRev);
  var rightY = Math.sin(screenAngleRev);
  var dotGR = rightX * gravityX  + rightY * gravityY;
  var rightGravity = dotGR / Math.sqrt(gravityX*gravityX+gravityY*gravityY+gravityZ*gravityZ);
  return -(90 - toDeg(Math.acos(rightGravity)));
}

    function relPosX(elem){
        return !elem.offsetParent ? elem.offsetLeft :
            elem.parentNode == elem.offsetParent ? elem.offsetLeft :
            elem.parentNode.offsetParent == elem.offsetParent ? elem.offsetLeft - elem.parentNode.offsetLeft :
            0;
    }
    function relPosY(elem){
        return !elem.offsetParent ? elem.offsetTop :
            elem.parentNode == elem.offsetParent ? elem.offsetTop :
            elem.parentNode.offsetParent == elem.offsetParent ? elem.offsetTop - elem.parentNode.offsetTop :
            0;
    }

    function parseCSSTransform(tformStr)
    {
        //http://www.w3.org/TR/css3-transforms/#transform-property
        var funStrs = tformStr.split(")");
        funStrs.pop();

        var mat = matNewIdentity();

        for(var i = 0; i < funStrs.length; ++i){

            var funNameValue = funStrs[i].split("(");
            var fun = funNameValue[0].trim();
            var args = funNameValue[1];
            switch(fun){
            // 2D Transform Functions
            // http://www.w3.org/TR/css3-transforms/#two-d-transform-functions
            case "matrix":
                matMul(mat, mat, matNewMatrix3x2.apply(null, args.split(",")));
                break;
            case "translate":
                var xy = args.split(",");
                matMul(mat, mat, matNewTranslate(parseFloat(xy[0]), parseFloat(xy[1] || "0")));
                break;
            case "translateX":
                matMul(mat, mat, matNewTranslate(parseFloat(args), 0));
                break;
            case "translateY":
                matMul(mat, mat, matNewTranslate(0, parseFloat(args)));
                break;
            case "scale":
                var sxy = args.split(",");
                matMul(mat, mat, matNewScale(parseFloat(sxy[0]), parseFloat(sxy.length >= 2 ? sxy[1] : sxy[0])));
                break;
            case "scaleX":
                matMul(mat, mat, matNewScale(parseFloat(args), 1));
                break;
            case "scaleY":
                matMul(mat, mat, matNewScale(1, parseFloat(args)));
                break;
            case "rotate":
                matMul(mat, mat, matNewRotate2D(toRadian(args)));
                break;
            case "skew":
                var wxy = args.split(",");
                matMul(mat, mat, matNewSkew2D(toRadian(wxy[0]), toRadian(wxy[1] || "0")));
                break;
            case "skewX":
                matMul(mat, mat, matNewSkew2D(toRadian(args), 0));
                break;
            case "skewY":
                matMul(mat, mat, matNewSkew2D(0, toRadian(args)));
                break;
            //http://www.w3.org/TR/css3-transforms/#three-d-transform-functions
            ///@todo support 3D Transform Functions
            }
        }
        return mat;
    }
    function toRadian(angle)
    {
        return angle.indexOf("deg") >= 0 ? parseFloat(angle) * (Math.PI/180) :
            angle.indexOf("grad") >= 0 ? parseFloat(angle) * (Math.PI/200) :
            parseFloat(angle);
    }

    function parseCSSTransformOrigin(originStr, boxSizes)
    {
        //http://www.w3.org/TR/css3-transforms/#transform-origin-property
        var values = originStr.split(" ");
        var origins = [];
        for(var i = 0; i < values.length; ++i){
            var value = values[i].trim().toLowerCase();
            if(value == ""){
                continue;
            }
            var refSize = boxSizes[origins.length] || 0;
            switch(value){
            case "left": origins.push(0); break;
            case "top": origins.push(0); break;
            case "right": origins.push(boxSizes[0] || 0); break;
            case "bottom": origins.push(boxSizes[1] || 0); break;
            case "center": origins.push(refSize*0.5); break;
            default:
                if(value.indexOf("%") > 0){
                    origins.push(refSize * parseFloat(value) / 100);
                }
                else{
                    origins.push(parseFloat(value));
                }
                break;
            }
        }

        while(origins.length < 2){
            refSize = boxSizes[origins.length] || 0;
            origins.push(refSize * 0.5); //default 50%
        }

        return origins;
    }

    function getElementComputedStyle(elem)
    {
        return window.getComputedStyle ? window.getComputedStyle(elem, "") :
            document.defaultView && document.defaultView.getComputedStyle ? document.defaultView.getComputedStyle(elem, "") :
            elem.currentStyle ||
            elem.style;
    }
    /// CSS Transformのプロパティ(transformプロパティやtransform-originプロパティなど)による変換行列を求めます。
    function getCSSTransformMatrix(elem)
    {
        var elemStyle = getElementComputedStyle(elem);
        var origins = parseCSSTransformOrigin(elemStyle.transformOrigin, [elem.offsetWidth, elem.offsetHeight]);
        var tform = parseCSSTransform(elemStyle.transform);
        return matNewMul(matNewTranslate(origins[0], origins[1]), matNewMul(tform, matNewTranslate(-origins[0], -origins[1])));
    }

    /// 要素内bounding-box左上を原点とする座標系からページ左上を原点とする座標系へ変換する行列を求めます。
    function getMatrixFromNodeToPage(elem)
    {
        var mat = matNewIdentity();
        while(elem){
            var tformMat = getCSSTransformMatrix(elem);
            if(tformMat){
                matMul(mat, tformMat, mat);
            }

            matMul(mat, matNewTranslate(relPosX(elem), relPosY(elem)), mat );
            var elemStyle = getElementComputedStyle(elem);
            if(elemStyle && elemStyle.position == "fixed"){ //see Firefox Bug https://bugzilla.mozilla.org/show_bug.cgi?id=434678
                matMul(mat, matNewTranslate(window.pageXOffset, window.pageYOffset), mat);
                break;
            }
            if(!elem.offsetParent){
                break; //root or body
            }
            elem = elem.parentNode;
        }
        return mat;
    }

    function convertPointFromPageToNode(elem, pageX, pageY)
    {
        if(global.webkitConvertPointFromPageToNode && global.WebKitPoint){
            // webkitConvertPointFromPageToNodeが使える場合はそれを使う！
            var r = webkitConvertPointFromPageToNode(elem, new WebKitPoint(pageX, pageY));
            return [r.x, r.y];
        }
        else{
            return convertPointFromPageToNode_Impl(elem, pageX, pageY);
        }
    }

    function convertPointFromPageToNode_Impl(elem, pageX, pageY)
    {
        var matPageToElement = matNewInverse(getMatrixFromNodeToPage(elem));
        if(matPageToElement){
            return matNewMulVec(matPageToElement, [pageX, pageY]);
        }
        else{
            return [0,0];
        }
    }

    /// 要素コンテンツ領域左上側の幅と高さを求めます。
    function getElementOuterLeftTop(elem)
    {
        var elemStyle = getElementComputedStyle(elem);
        function getNumber(propName){ return parseFloat(elemStyle.getPropertyValue(propName));}
        var left = getNumber("border-left-width") + getNumber("padding-left") || 0;
        var top = getNumber("border-top-width") + getNumber("padding-top") || 0;
        return [left, top];
    }

    // ページ座標から要素内コンテンツ領域左上を原点とする座標系へ変換します。
    function convertPointFromPageToNodeContentArea(elem, pageX, pageY)
    {
        var outerLeftTop = getElementOuterLeftTop(elem);
        var pos = convertPointFromPageToNode(elem, pageX, pageY);
        pos[0] -= outerLeftTop[0];
        pos[1] -= outerLeftTop[1];
        return pos;
    }