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| class Math3d {
//by ericlin
// (oui, c'est un fichier trouvé sur le net car ce sont des fonctions mathématiques bien au dessus de mon niveau)
static function vector(proxPoint, distPoint) {
var x = distPoint.x-proxPoint.x;
var y = distPoint.y-proxPoint.y;
var z = distPoint.z-proxPoint.z;
return {x:x, y:y, z:z};
}
static function getLength(vector1) {
var a1 = vector1.x;
var b1 = vector1.y;
var c1 = vector1.z;
return Math.sqrt(a1*a1+b1*b1+c1*c1);
}
static function isZero(floatNumber) {
//to serve as "==" for floatNumber; ->Flash has inaccuracy
if (Math.abs(floatNumber)<0.00001) {
return true;
}
return false;
}
static function getMidPoint(point1, point2) {
var a1 = point1.x;
var b1 = point1.y;
var c1 = point1.z;
var a2 = point2.x;
var b2 = point2.y;
var c2 = point2.z;
return {x:(a1+a2)/2, y:(b1+b2)/2, z:(c1+c2)/2};
}
static function distance(pt1, pt2) {
var dy = pt2.y-pt1.y;
var dx = pt2.x-pt1.x;
return Math.sqrt(dy*dy+dx*dx);
}
//=========================================
static function getAngle(vector1, vector2) {
var a1 = vector1.x;
var b1 = vector1.y;
var c1 = vector1.z;
var a2 = vector2.x;
var b2 = vector2.y;
var c2 = vector2.z;
var dotP = (a1*a2+b1*b2+c1*c2);
var cos = dotP/(getLength(vector1)*getLength(vector2));
//trace("dotP="+dotP+", len1="+getLength(vector1)+",len2="+getLength(vector2)+",cos="+cos);
var sin2 = 1-cos*cos;
if (sin2<0) {
trace(" wrong "+cos);
sin2 = 0;
}
//I took long time to find this bug. Who can guess that (1-cos*cos) is negative ?!
//sqrt returns a NaN for a negative value !
return Math.atan2(Math.sqrt(sin2), cos);
}
//=====================================
static function getRotateAxis(vector1, vector2) {
//get the axis that perpendicular to the plane formed by vector1 and vector2;
//the answer is not unique. At least, the negative axis will also be an answer.
//if two vectors are in line, then the answer would be a plane.
//Here just get one of them out for use. No attemp to get all of them.
var a1 = vector1.x;
var b1 = vector1.y;
var c1 = vector1.z;
var a2 = vector2.x;
var b2 = vector2.y;
var c2 = vector2.z;
var x, y, z;
//solve this two equations: since dotProduct should be 0;
//a1*x+b1.y+c1*z=0;
//a2*x+b2*y+c2*z=0
if (!isZero(a1*b2-b1*a2)) {
z = 1;
y = (c1*a2-c2*a1)/(a1*b2-a2*b1);
x = (c1*b2-c2*b1)/(b1*a2-b2*a1);
return {x:x, y:y, z:z};
}
z = 0;
//z=0, axis in xy plane;
if (!isZero(a1)) {
y = 1;
x = -b1/a1;
return {x:x, y:y, z:z};
}
// it is X axis;
y = 0;
x = 1;
return {x:x, y:y, z:z};
}
//=========================================
static function getRotateAngle(axis, vector1, vector2) {
var angle = getAngle(vector1, vector2);
var test = {x:vector1.x, y:vector1.y, z:vector1.z};
rotate3d(test, axis, angle);
var angle2 = getAngle(test, vector2);
if (isZero(angle2)) {
trace("posi angle");
return angle;
}
//------------for sure, I confirm it. If you dare, you might just return -angle without recheck.
test = {x:vector1.x, y:vector1.y, z:vector1.z};
rotate3d(test, axis, -angle);
angle2 = getAngle(test, vector2);
if (isZero(angle2)) {
trace("nega angle");
return -angle;
}
trace("no match");
return null;
}
//====================================================
static function rotate2d(x, y, pAngle) {
var sin = Math.sin(pAngle);
var cos = Math.cos(pAngle);
return {x:x*cos-y*sin, y:x*sin+y*cos};
}
static function rotate3d(point, axis, pAngle) {
//permantantly change the point data but preserved the axis data
//axis={x: ,y: ,z}
var vAxis = {x:axis.x, y:axis.y, z:axis.z};
//copy to preserve original one
//rotate around X axis:
var xRot = Math.atan2(vAxis.y, vAxis.z);
if (xRot != 0) {
var pt = rotate2d(vAxis.z, vAxis.y, -xRot);
vAxis.z=pt.x, vAxis.y=pt.y;
var pt = rotate2d(point.z, point.y, -xRot);
point.z=pt.x, point.y=pt.y;
}
//now on z, x plane;
var yRot = Math.atan2(vAxis.z, vAxis.x);
if (yRot != 0) {
//var pt = rotate2d(vAxis.x, vAxis.z, -yRot);
//vAxis.x=pt.x, vAxis.z=pt.y;
var pt = rotate2d(point.x, point.z, -yRot);
point.x=pt.x, point.z=pt.y;
}
//now on vAxis is the X axis;
var pt = rotate2d(point.z, point.y, pAngle);
point.z=pt.x, point.y=pt.y;
//rotate back to original vAxis;
if (yRot != 0) {
var pt = rotate2d(point.x, point.z, yRot);
point.x=pt.x, point.z=pt.y;
}
if (xRot != 0) {
var pt = rotate2d(point.z, point.y, xRot);
point.z=pt.x, point.y=pt.y;
}
}
//----------------------------------
static function rotate3dArray(points, axis, pAngle) {
//modify so that we dont repeatedly calculate sin cos for each point
//it is about 3 times faster than call rotate once per point, but here only 8 point, so it short from 6msec to 2 msec only
//axis={x: ,y: ,z}
var vAxis = {x:axis.x, y:axis.y, z:axis.z};
//rotate around X axis:
var xRot = Math.atan2(vAxis.y, vAxis.z);
var sinX = Math.sin(-xRot);
var cosX = Math.cos(-xRot);
var pt = {z:vAxis.z*cosX-vAxis.y*sinX, y:vAxis.z*sinX+vAxis.y*cosX};
pt.x = vAxis.x;
vAxis = pt;
var yRot = Math.atan2(vAxis.z, vAxis.x);
var sinY = Math.sin(-yRot);
var cosY = Math.cos(-yRot);
var sinA = Math.sin(pAngle);
var cosA = Math.cos(pAngle);
//---------------------------------
for (var i = 0; i<points.length; i++) {
var point = points[i];
var pt = {x:point.z*cosX-point.y*sinX, y:point.z*sinX+point.y*cosX};
point.z=pt.x, point.y=pt.y;
var pt = {x:point.x*cosY-point.z*sinY, y:point.x*sinY+point.z*cosY};
point.x=pt.x, point.z=pt.y;
var pt = {x:point.z*cosA-point.y*sinA, y:point.z*sinA+point.y*cosA};
point.z=pt.x, point.y=pt.y;
var pt = {x:point.x*cosY-point.z*-sinY, y:point.x*-sinY+point.z*cosY};
point.x=pt.x, point.z=pt.y;
var pt = {x:point.z*cosX-point.y*-sinX, y:point.z*-sinX+point.y*cosX};
point.z=pt.x, point.y=pt.y;
}
}
//====================================================
static function skew(parent, child, mcW, mcH, ptTL, ptBL, ptTR) {
//child and parent registration point must at the top left
//mcW, mcH => the dimension of the child, it is not necessarily to be the real width and height;
//TL: top_left, BL: bottom_left, TR: top_right
var angleP2 = Math.atan2(ptTR.y-ptTL.y, ptTR.x-ptTL.x);
var angleP1 = Math.atan2(ptBL.y-ptTL.y, ptBL.x-ptTL.x);
var dAngle = (angleP1-angleP2)/2;
var arm = 1/(Math.sqrt(2)*Math.cos(dAngle));
parent._x = ptTL.x;
parent._y = ptTL.y;
parent._xscale = 100;
parent._rotation = (180/Math.PI)*(angleP1-dAngle);
child._rotation = -45;
parent._yscale = 100*Math.tan(dAngle);
child._xscale = distance(ptTR, ptTL)*100/arm/mcW;
child._yscale = distance(ptBL, ptTL)*100/arm/mcH;
}
} |
3d problème perspective
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