Reproduction
3D version of "Knots", a woodcut by M. C. Escher
http://www.mcescher.com/Gallery/recogn-bmp/LW444.jpg http://image53.webshots.com/653/1/85/61/2927185610096556516dtSNna_fs.jpg
Light source follows mouse, drag to rotate.
/**
* Copyright yonatan ( http://wonderfl.net/user/yonatan )
* MIT License ( http://www.opensource.org/licenses/mit-license.php )
* Downloaded from: http://wonderfl.net/c/4BF9
*/
// forked from yonatan's MCE on SiGL
// forked from keim_at_Si's wonderflで3D 【Phong shading】
// forked from keim_at_Si's wonderflで3D 【Flat shading】 高速化
// forked from keim_at_Si's wonderflで3D 【Flat shading】
// 高速化，マウスで光源移動，クリックで材質変更
//--------------------------------------------------
package {
import flash.display.*;
import flash.text.*;
import flash.geom.*;
import flash.events.*;
import flash.utils.*;
import flash.filters.*;
import flash.ui.*;
// import net.hires.debug.Stats;
[SWF(width="465", height="465", backgroundColor="0xE0E0E0", frameRate="30")]
public class main extends Sprite {
private const _sides:int = 4;
private const _sections:int = 72;
private var _matrix:Matrix3D = new Matrix3D();
private var _rotMatrix:Matrix3D = new Matrix3D();
private var _engine:EngineFaceBasedRender = new EngineFaceBasedRender(800, _sections*_sides*8);
private var _material:Material = new Material;
private var _light:Light = new Light();
private var _models:Array = [];
private var _model:Knot;
private var _transformedSideNormals:Vector.<Number> = new Vector.<Number>();
private var _mousePoint:Point;
private var _timeSum:int, _timeCount:int;
private var _textField:TextField = new TextField();
function main() {
var i:int;
for (i=0; i<60; i++) _models.push(new Knot(2, 3, _sections, _sides, 2/3, i/60));
stage.quality = "medium";
_engine.x = 232;
_engine.y = 232;
// GlowFilter(color:uint = 0xFF0000, alpha:Number = 1.0, blurX:Number = 6.0, blurY:Number = 6.0,
// strength:Number = 2, quality:int = 1, inner:Boolean = false, knockout:Boolean = false)
_engine.filters = [new GlowFilter(0, 1, 4, 4, 2, 2)];
addChild(_engine);
addEventListener("enterFrame", _onEnterFrame);
Mouse.cursor = MouseCursor.BUTTON;
stage.addEventListener("mouseDown", function(e:Event):void {
_mousePoint = new Point(mouseX, mouseY);
Mouse.cursor = MouseCursor.HAND;
});
stage.addEventListener("mouseUp", function(e:Event):void {
_mousePoint = null;
Mouse.cursor = MouseCursor.BUTTON;
});
// initialize parameters
// _timeSum = 0;
// _timeCount = 0;
// _textField.autoSize = "left";
// _textField.background = true;
// _textField.backgroundColor = 0x80f080;
// addChild(_textField);
// var status:Stats = new Stats();
// status.x = 400;
// addChild(status);
}
private function _onEnterFrame(e:Event) : void {
var i:int, t:int;
_model = _models[int(getTimer()/10) % _models.length];
// update paremters
if(_mousePoint) {
var p:Point = new Point(mouseX, mouseY).subtract(_mousePoint);
var axis:Vector3D = new Vector3D(p.y, -p.x, 0);
axis.normalize();
_rotMatrix.appendRotation(p.length/2, axis)
_mousePoint.x = mouseX;
_mousePoint.y = mouseY;
}
// light position
var lx:Number = (Math.max(0, Math.min(2, mouseX / (465 / 2))) - 1) / Math.SQRT2;
var ly:Number = (Math.max(0, Math.min(2, mouseY / (465 / 2))) - 1) / Math.SQRT2;
var lz:Number = -Math.sqrt(1 - (lx*lx+ly*ly));
_light.setPosition(lx, ly, lz);
t = getTimer();
_engine.pushMatrix();
_matrix.identity();
_matrix.append(_rotMatrix);
_matrix.appendScale(10, 10, 10);
_matrix.appendTranslation(0, 0, 150);
_engine.matrix.append(_matrix);
_engine.project(_model);
_calculateVertexNormal();
_engine.render(_model, _light, _material);
_engine.popMatrix();
_timeSum += getTimer() - t;
// if (++_timeCount == 30) {
// _textField.text = "Redering time: " + String(_timeSum) + "[ms/30frames]";
// _timeSum = 0;
// _timeCount = 0;
// }
}
private function _calculateVertexNormal() : void {
var len:int = _transformedSideNormals.length;
var ni:int = 0;
var ti:int = 0;
_rotMatrix.transformVectors(_model.sideNormals, _transformedSideNormals);
while (ni<len) {
var nx:Number = _transformedSideNormals[ni++];
var ny:Number = _transformedSideNormals[ni++];
var nz:Number = _transformedSideNormals[ni++];
var v:Vector3D = _light.direction;
var intensity:Number = v.x * nx + v.y * ny + v.z * nz;
intensity *= intensity;
//if(intensity<0) intensity = -intensity; // saturate
if(nz>0) intensity = -intensity; // front/back material
var u:Number = 0.5 + intensity/2;
_model.texCoord[ti] = u; ti+=3;
_model.texCoord[ti] = u; ti+=3;
_model.texCoord[ti] = u; ti+=3;
_model.texCoord[ti] = u; ti+=3;
}
}
}
}
import flash.display.*;
import flash.filters.*;
import flash.geom.*;
class EngineFaceBasedRender extends Shape {
public var matrix:Matrix3D;
private var _vertexOnWorld:Vector.<Number>;
private var _vout:Vector.<Number>;
private var _projector:PerspectiveProjection;
private var _projectionMatrix:Matrix3D;
private var _matrixStac:Vector.<Matrix3D>;
function EngineFaceBasedRender(focus:Number=400, numVerts:int = 0) {
_vertexOnWorld = new Vector.<Number>(numVerts*3, numVerts != 0);
_vout = new Vector.<Number>;
_projector = new PerspectiveProjection();
_matrixStac = new Vector.<Matrix3D>();
initialize(focus);
}
public function initialize(focus:Number) : EngineFaceBasedRender {
_projector.focalLength = focus;
_projectionMatrix = _projector.toMatrix3D();
matrix = new Matrix3D();
_matrixStac.length = 1;
_matrixStac[0] = matrix;
return this;
}
public function clearMatrix() : EngineFaceBasedRender {
matrix = _matrixStac[0];
_matrixStac.length = 1;
return this;
}
public function pushMatrix() : EngineFaceBasedRender {
_matrixStac.push(matrix.clone());
return this;
}
public function popMatrix() : EngineFaceBasedRender {
if (_matrixStac.length == 1) return this;
matrix = _matrixStac.pop();
return this;
}
public function project(model:Model) : EngineFaceBasedRender {
matrix.transformVectors(model.vertices, _vertexOnWorld);
var vertices:Vector.<Number> = _vertexOnWorld;
for each (var face:Face in model.faces) {
var z:Number;
z = vertices[int(int((face.i0<<1) + face.i0) + 2)];
z += vertices[int(int((face.i1<<1) + face.i1) + 2)];
z += vertices[int(int((face.i2<<1) + face.i2) + 2)];
face.z = z;
}
model.faces.sort(function(f1:Face, f2:Face) : Number { return f2.z - f1.z; });
return this;
}
public function render(model:Model, light:Light, material:Material) : EngineFaceBasedRender {
Utils3D.projectVectors(_projectionMatrix, _vertexOnWorld, _vout, model.texCoord);
graphics.clear();
graphics.beginBitmapFill(material.texture, null, false, true);
graphics.drawTriangles(_vout, model.indices, model.texCoord);
graphics.endFill();
return this;
}
}
class Face {
public var i0:int, i1:int, i2:int, z:Number;
// Factory
static private var _freeList:Vector.<Face> = new Vector.<Face>();
static public function alloc() : Face { return _freeList.pop() || new Face(); }
static public function free(face:Face) : void { _freeList.push(face); }
}
class Model {
public var vertices:Vector.<Number>;
public var texCoord:Vector.<Number>;
public var faces:Vector.<Face>;
private var _indices:Vector.<int> = new Vector.<int>();
private var _faceIdx:int = 0;
function Model(vertices:Vector.<Number>=null, texCoord:Vector.<Number>=null, faces:Vector.<Face>=null) {
this.vertices = vertices || new Vector.<Number>();
this.texCoord = texCoord || new Vector.<Number>();
this.faces = faces || new Vector.<Face>();
if(faces) {
_indices = new Vector.<int>(faces.length*3, true);
}
}
public function clear() : Model {
for each (var face:Face in faces) Face.free(face);
faces = new Vector.<Face>();
_faceIdx = 0;
return this;
}
public function face(i0:int, i1:int, i2:int) : Model {
var face:Face = Face.alloc();
face.i0 = i0;
face.i1 = i1;
face.i2 = i2;
faces[_faceIdx++] = face;
return this;
}
public function get indices() : Vector.<int> {
var i:int = 0;
for each (var face:Face in faces) {
_indices[i++] = face.i0;
_indices[i++] = face.i1;
_indices[i++] = face.i2;
}
return _indices;
}
}
class Light {
private var _direction:Vector3D = new Vector3D();
private var _halfVector:Vector3D = new Vector3D();
public function get direction() : Vector3D { return _direction; }
public function get halfVector() : Vector3D { return _halfVector; }
function Light(x:Number=1, y:Number=1, z:Number=1) { setPosition(x, y, z); }
public function setPosition(x:Number, y:Number, z:Number) : void {
_direction.x = -x;
_direction.y = -y;
_direction.z = -z;
_direction.normalize();
_halfVector.x = _direction.x;
_halfVector.y = _direction.y;
_halfVector.z = _direction.z + 1;
_halfVector.normalize();
}
}
class Material {
private static const LINES:int = 13;
private static const W:int = 0x800;
private static const H:int = 0x100;
public var texture:BitmapData = new BitmapData(W,H,false);
private var _shape:Shape = new Shape;
function Material() { setColor(0xdb9438, 0xb2a64a); }
protected function _drawLines(color:uint, start:Number, end:Number):void {
for(var line:int = 0; line<LINES; line++) {
var y1:Number = line/LINES*H;
var y2:Number = (line+1)/LINES*H;
_shape.graphics.beginFill(color);
_shape.graphics.moveTo(start*W, y1)
_shape.graphics.lineTo(end*W, (y1+y2)/2)
_shape.graphics.lineTo(start*W, y2)
_shape.graphics.endFill();
}
}
public function setColor(front:uint, back:uint) : Material
{
_shape.graphics.clear();
_shape.graphics.beginFill(back);
_shape.graphics.drawRect(0, 0, W/2, H);
_shape.graphics.endFill();
_shape.graphics.beginFill(front);
_shape.graphics.drawRect(W/2, 0, W/2, H);
_shape.graphics.endFill();
_drawLines(0xFFFFFF, 9/8, 6/7);
_drawLines(0, 1/2, 6/7-0.025);
_drawLines(0, 1/2, -1/4);
texture.draw(_shape, null, null, null, null, true);
texture.applyFilter(texture, texture.rect, new Point, new BlurFilter(4,4,3));
return this;
}
static public function calculateTexCoord(texCoord:Point, light:Light, normal:Vector3D, doubleSided:Boolean=false) : void {
var v:Vector3D = light.direction;
texCoord.x = v.x * normal.x + v.y * normal.y + v.z * normal.z;
if (texCoord.x < 0) texCoord.x = (doubleSided) ? -texCoord.x : 0;
v = light.halfVector;
texCoord.y = v.x * normal.x + v.y * normal.y + v.z * normal.z;
if (texCoord.y < 0) texCoord.y = (doubleSided) ? -texCoord.y : 0;
}
}
class Knot extends Model {
private var _p:int, _q:int, _sections:int, _slices:int, _sides:int, _thickness:Number, _offset:Number;
public var sideNormals:Vector.<Number>;
public function Knot(p:int = 2, q:int = 3, sections:int = 72, sides:int = 4, thickness:Number = 2/3, offset:Number = 0) {
var numVerts:int = sections*sides*8;
_p = p;
_q = q;
_sections = sections;
_slices = sections * 2;
_sides = sides;
_thickness = thickness;
_offset = offset;
super(
new Vector.<Number>(numVerts*3, true),
new Vector.<Number>(numVerts*3, true),
new Vector.<Face>(sections*sides*8, true)
);
sideNormals = new Vector.<Number>(_slices*_sides*3, true)
_createVertices();
_createFaces();
_createNormals();
}
protected function _createNormals():void {
var i:int = 0;
for(var section:int=0; section<_sections; section++) {
for(var side:int=0; side<_sides; side++) {
for(var slice:int=0; slice<2; slice++) {
var u:Number = Math.PI*2 * (section*2+slice)/_slices;
var v:Number = Math.PI*2 * side/_sides - u*(_sides-1)/_sides;
var n:Vector3D = _extrudedPoint(u, v, 1);
n.decrementBy(_curvePoint(u));
n.normalize();
sideNormals[i++] = n.x;
sideNormals[i++] = n.y;
sideNormals[i++] = n.z;
}
}
}
}
protected function _createFaces():void {
for(var section:int=0; section<_sections; section++) {
for(var side:int=0; side<_sides; side++) {
var i:int = section*_sides*8 + side*8;
// section
face(i+1, i+0, i+4).face(i+4, i+5, i+1)
i++;
face(i+1, i+0, i+4).face(i+4, i+5, i+1)
i++;
face(i+1, i+0, i+4).face(i+4, i+5, i+1)
i--; i--;
// connector
var i0:int, i1:int, i2:int, i3:int;
i0=i+5; i1=i+6;
i += _sides*8;
if(section+1 == _sections) {
i+=8; // compensate for twist
if(side+1 == _sides) i = 0;
}
i %= vertices.length/3;
i2=i+1; i3=i+2;
face(i0, i2, i1); face(i2, i3, i1);
}
}
}
protected function _createVertices():void {
var i:int = 0;
function _vertex(v:Vector3D, texv:Number):void {
vertices[i] = v.x; texCoord[i++] = 0;
vertices[i] = v.y; texCoord[i++] = texv;
vertices[i] = v.z; texCoord[i++] = 0;
}
for(var section:int=0; section<_sections; section++) {
for(var side:int=0; side<_sides; side++) {
var p:Number;
for each(p in [0, 0.4, 0.6, 1]) _vertex(_edgePoint(section*2, side, p), p);
for each(p in [0, 0.4, 0.6, 1]) _vertex(_edgePoint(section*2+1, side, p), p);
}
}
}
// 0 <= p <= 1 is the offset along the edge
protected function _edgePoint(slice:int, side:int, p:Number):Vector3D {
var u:Number = Math.PI*2 * slice/_slices;
var v:Number = Math.PI*2 * side/_sides - u*(_sides-1)/_sides;
v -= Math.PI / _sides; // make side 0 parallel to Z axis
var v0:Vector3D = _extrudedPoint(u, v, _thickness);
var v1:Vector3D = _extrudedPoint(u, v + Math.PI*2/_sides, _thickness);
return _vlerp(v0, v1, p);
}
protected function _extrudedPoint(u:Number, v:Number, length:Number):Vector3D {
v -= Math.PI*2*_offset/_sections*(_sides-1)/_sides;
// calculate curve point and normal vectors from u
var cp:Vector3D = _curvePoint(u);
var ncp:Vector3D = _curvePoint(u+0.0001);
var t:Vector3D = ncp.subtract(cp);
var n:Vector3D = ncp.add(cp);
var b:Vector3D = t.crossProduct(n);
n = b.crossProduct(t);
n.normalize();
b.normalize();
// extrude in direction v
var cx:Number = length * Math.sin(v);
var cy:Number = length * -Math.cos(v);
return new Vector3D(
cp.x + cx*n.x + cy*b.x,
cp.y + cx*n.y + cy*b.y,
cp.z + cx*n.z + cy*b.z
);
}
protected function _curvePoint(t:Number):Vector3D {
t += Math.PI*2*_offset/_sections;
return new Vector3D(
2 * Math.sin(t*_p) - Math.sin(t),
-(2 * Math.cos(t*_p) + Math.cos(t)),
Math.sin(t*_q)
);
}
protected function _vlerp(v0:Vector3D, v1:Vector3D, p:Number):Vector3D {
return new Vector3D(
v0.x*(1-p) + v1.x*p,
v0.y*(1-p) + v1.y*p,
v0.z*(1-p) + v1.z*p,
v0.w*(1-p) + v1.w*p
);
}
}