1 | define(["./_base","dojo/_base/lang"], |
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2 | function(g, lang){ |
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3 | var m = g.matrix = {}; |
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4 | |
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5 | // candidates for dojox.math: |
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6 | var _degToRadCache = {}; |
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7 | m._degToRad = function(degree){ |
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8 | return _degToRadCache[degree] || (_degToRadCache[degree] = (Math.PI * degree / 180)); |
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9 | }; |
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10 | m._radToDeg = function(radian){ return radian / Math.PI * 180; }; |
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11 | |
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12 | m.Matrix2D = function(arg){ |
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13 | // summary: |
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14 | // a 2D matrix object |
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15 | // description: |
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16 | // Normalizes a 2D matrix-like object. If arrays is passed, |
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17 | // all objects of the array are normalized and multiplied sequentially. |
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18 | // arg: Object |
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19 | // a 2D matrix-like object, a number, or an array of such objects |
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20 | if(arg){ |
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21 | if(typeof arg == "number"){ |
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22 | this.xx = this.yy = arg; |
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23 | }else if(arg instanceof Array){ |
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24 | if(arg.length > 0){ |
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25 | var matrix = m.normalize(arg[0]); |
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26 | // combine matrices |
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27 | for(var i = 1; i < arg.length; ++i){ |
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28 | var l = matrix, r = m.normalize(arg[i]); |
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29 | matrix = new m.Matrix2D(); |
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30 | matrix.xx = l.xx * r.xx + l.xy * r.yx; |
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31 | matrix.xy = l.xx * r.xy + l.xy * r.yy; |
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32 | matrix.yx = l.yx * r.xx + l.yy * r.yx; |
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33 | matrix.yy = l.yx * r.xy + l.yy * r.yy; |
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34 | matrix.dx = l.xx * r.dx + l.xy * r.dy + l.dx; |
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35 | matrix.dy = l.yx * r.dx + l.yy * r.dy + l.dy; |
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36 | } |
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37 | lang.mixin(this, matrix); |
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38 | } |
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39 | }else{ |
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40 | lang.mixin(this, arg); |
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41 | } |
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42 | } |
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43 | }; |
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44 | |
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45 | // the default (identity) matrix, which is used to fill in missing values |
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46 | lang.extend(m.Matrix2D, {xx: 1, xy: 0, yx: 0, yy: 1, dx: 0, dy: 0}); |
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47 | |
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48 | lang.mixin(m, { |
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49 | // summary: |
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50 | // class constants, and methods of dojox/gfx/matrix |
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51 | |
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52 | // matrix constants |
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53 | |
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54 | // identity: dojox/gfx/matrix.Matrix2D |
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55 | // an identity matrix constant: identity * (x, y) == (x, y) |
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56 | identity: new m.Matrix2D(), |
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57 | |
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58 | // flipX: dojox/gfx/matrix.Matrix2D |
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59 | // a matrix, which reflects points at x = 0 line: flipX * (x, y) == (-x, y) |
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60 | flipX: new m.Matrix2D({xx: -1}), |
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61 | |
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62 | // flipY: dojox/gfx/matrix.Matrix2D |
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63 | // a matrix, which reflects points at y = 0 line: flipY * (x, y) == (x, -y) |
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64 | flipY: new m.Matrix2D({yy: -1}), |
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65 | |
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66 | // flipXY: dojox/gfx/matrix.Matrix2D |
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67 | // a matrix, which reflects points at the origin of coordinates: flipXY * (x, y) == (-x, -y) |
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68 | flipXY: new m.Matrix2D({xx: -1, yy: -1}), |
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69 | |
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70 | // matrix creators |
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71 | |
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72 | translate: function(a, b){ |
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73 | // summary: |
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74 | // forms a translation matrix |
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75 | // description: |
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76 | // The resulting matrix is used to translate (move) points by specified offsets. |
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77 | // a: Number|dojox/gfx.Point |
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78 | // an x coordinate value, or a point-like object, which specifies offsets for both dimensions |
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79 | // b: Number? |
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80 | // a y coordinate value |
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81 | // returns: dojox/gfx/matrix.Matrix2D |
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82 | if(arguments.length > 1){ |
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83 | return new m.Matrix2D({dx: a, dy: b}); // dojox/gfx/matrix.Matrix2D |
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84 | } |
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85 | // branch |
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86 | return new m.Matrix2D({dx: a.x, dy: a.y}); // dojox/gfx/matrix.Matrix2D |
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87 | }, |
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88 | scale: function(a, b){ |
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89 | // summary: |
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90 | // forms a scaling matrix |
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91 | // description: |
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92 | // The resulting matrix is used to scale (magnify) points by specified offsets. |
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93 | // a: Number|dojox/gfx.Point |
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94 | // a scaling factor used for the x coordinate, or |
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95 | // a uniform scaling factor used for the both coordinates, or |
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96 | // a point-like object, which specifies scale factors for both dimensions |
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97 | // b: Number? |
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98 | // a scaling factor used for the y coordinate |
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99 | // returns: dojox/gfx/matrix.Matrix2D |
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100 | if(arguments.length > 1){ |
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101 | return new m.Matrix2D({xx: a, yy: b}); // dojox/gfx/matrix.Matrix2D |
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102 | } |
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103 | if(typeof a == "number"){ |
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104 | return new m.Matrix2D({xx: a, yy: a}); // dojox/gfx/matrix.Matrix2D |
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105 | } |
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106 | return new m.Matrix2D({xx: a.x, yy: a.y}); // dojox/gfx/matrix.Matrix2D |
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107 | }, |
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108 | rotate: function(angle){ |
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109 | // summary: |
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110 | // forms a rotating matrix |
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111 | // description: |
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112 | // The resulting matrix is used to rotate points |
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113 | // around the origin of coordinates (0, 0) by specified angle. |
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114 | // angle: Number |
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115 | // an angle of rotation in radians (>0 for CW) |
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116 | // returns: dojox/gfx/matrix.Matrix2D |
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117 | var c = Math.cos(angle); |
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118 | var s = Math.sin(angle); |
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119 | return new m.Matrix2D({xx: c, xy: -s, yx: s, yy: c}); // dojox/gfx/matrix.Matrix2D |
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120 | }, |
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121 | rotateg: function(degree){ |
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122 | // summary: |
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123 | // forms a rotating matrix |
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124 | // description: |
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125 | // The resulting matrix is used to rotate points |
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126 | // around the origin of coordinates (0, 0) by specified degree. |
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127 | // See dojox/gfx/matrix.rotate() for comparison. |
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128 | // degree: Number |
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129 | // an angle of rotation in degrees (>0 for CW) |
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130 | // returns: dojox/gfx/matrix.Matrix2D |
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131 | return m.rotate(m._degToRad(degree)); // dojox/gfx/matrix.Matrix2D |
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132 | }, |
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133 | skewX: function(angle) { |
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134 | // summary: |
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135 | // forms an x skewing matrix |
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136 | // description: |
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137 | // The resulting matrix is used to skew points in the x dimension |
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138 | // around the origin of coordinates (0, 0) by specified angle. |
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139 | // angle: Number |
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140 | // a skewing angle in radians |
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141 | // returns: dojox/gfx/matrix.Matrix2D |
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142 | return new m.Matrix2D({xy: Math.tan(angle)}); // dojox/gfx/matrix.Matrix2D |
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143 | }, |
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144 | skewXg: function(degree){ |
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145 | // summary: |
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146 | // forms an x skewing matrix |
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147 | // description: |
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148 | // The resulting matrix is used to skew points in the x dimension |
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149 | // around the origin of coordinates (0, 0) by specified degree. |
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150 | // See dojox/gfx/matrix.skewX() for comparison. |
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151 | // degree: Number |
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152 | // a skewing angle in degrees |
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153 | // returns: dojox/gfx/matrix.Matrix2D |
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154 | return m.skewX(m._degToRad(degree)); // dojox/gfx/matrix.Matrix2D |
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155 | }, |
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156 | skewY: function(angle){ |
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157 | // summary: |
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158 | // forms a y skewing matrix |
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159 | // description: |
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160 | // The resulting matrix is used to skew points in the y dimension |
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161 | // around the origin of coordinates (0, 0) by specified angle. |
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162 | // angle: Number |
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163 | // a skewing angle in radians |
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164 | // returns: dojox/gfx/matrix.Matrix2D |
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165 | return new m.Matrix2D({yx: Math.tan(angle)}); // dojox/gfx/matrix.Matrix2D |
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166 | }, |
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167 | skewYg: function(degree){ |
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168 | // summary: |
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169 | // forms a y skewing matrix |
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170 | // description: |
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171 | // The resulting matrix is used to skew points in the y dimension |
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172 | // around the origin of coordinates (0, 0) by specified degree. |
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173 | // See dojox/gfx/matrix.skewY() for comparison. |
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174 | // degree: Number |
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175 | // a skewing angle in degrees |
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176 | // returns: dojox/gfx/matrix.Matrix2D |
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177 | return m.skewY(m._degToRad(degree)); // dojox/gfx/matrix.Matrix2D |
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178 | }, |
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179 | reflect: function(a, b){ |
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180 | // summary: |
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181 | // forms a reflection matrix |
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182 | // description: |
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183 | // The resulting matrix is used to reflect points around a vector, |
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184 | // which goes through the origin. |
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185 | // a: dojox/gfx.Point|Number |
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186 | // a point-like object, which specifies a vector of reflection, or an X value |
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187 | // b: Number? |
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188 | // a Y value |
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189 | // returns: dojox/gfx/matrix.Matrix2D |
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190 | if(arguments.length == 1){ |
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191 | b = a.y; |
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192 | a = a.x; |
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193 | } |
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194 | // make a unit vector |
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195 | var a2 = a * a, b2 = b * b, n2 = a2 + b2, xy = 2 * a * b / n2; |
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196 | return new m.Matrix2D({xx: 2 * a2 / n2 - 1, xy: xy, yx: xy, yy: 2 * b2 / n2 - 1}); // dojox/gfx/matrix.Matrix2D |
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197 | }, |
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198 | project: function(a, b){ |
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199 | // summary: |
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200 | // forms an orthogonal projection matrix |
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201 | // description: |
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202 | // The resulting matrix is used to project points orthogonally on a vector, |
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203 | // which goes through the origin. |
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204 | // a: dojox/gfx.Point|Number |
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205 | // a point-like object, which specifies a vector of projection, or |
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206 | // an x coordinate value |
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207 | // b: Number? |
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208 | // a y coordinate value |
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209 | // returns: dojox/gfx/matrix.Matrix2D |
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210 | if(arguments.length == 1){ |
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211 | b = a.y; |
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212 | a = a.x; |
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213 | } |
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214 | // make a unit vector |
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215 | var a2 = a * a, b2 = b * b, n2 = a2 + b2, xy = a * b / n2; |
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216 | return new m.Matrix2D({xx: a2 / n2, xy: xy, yx: xy, yy: b2 / n2}); // dojox/gfx/matrix.Matrix2D |
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217 | }, |
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218 | |
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219 | // ensure matrix 2D conformance |
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220 | normalize: function(matrix){ |
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221 | // summary: |
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222 | // converts an object to a matrix, if necessary |
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223 | // description: |
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224 | // Converts any 2D matrix-like object or an array of |
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225 | // such objects to a valid dojox/gfx/matrix.Matrix2D object. |
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226 | // matrix: Object |
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227 | // an object, which is converted to a matrix, if necessary |
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228 | // returns: dojox/gfx/matrix.Matrix2D |
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229 | return (matrix instanceof m.Matrix2D) ? matrix : new m.Matrix2D(matrix); // dojox/gfx/matrix.Matrix2D |
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230 | }, |
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231 | |
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232 | // common operations |
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233 | |
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234 | isIdentity: function(matrix){ |
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235 | // summary: |
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236 | // returns whether the specified matrix is the identity. |
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237 | // matrix: dojox/gfx/matrix.Matrix2D |
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238 | // a 2D matrix object to be tested |
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239 | // returns: Boolean |
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240 | return matrix.xx == 1 && matrix.xy == 0 && matrix.yx == 0 && matrix.yy == 1 && matrix.dx == 0 && matrix.dy == 0; // Boolean |
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241 | }, |
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242 | clone: function(matrix){ |
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243 | // summary: |
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244 | // creates a copy of a 2D matrix |
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245 | // matrix: dojox/gfx/matrix.Matrix2D |
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246 | // a 2D matrix-like object to be cloned |
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247 | // returns: dojox/gfx/matrix.Matrix2D |
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248 | var obj = new m.Matrix2D(); |
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249 | for(var i in matrix){ |
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250 | if(typeof(matrix[i]) == "number" && typeof(obj[i]) == "number" && obj[i] != matrix[i]) obj[i] = matrix[i]; |
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251 | } |
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252 | return obj; // dojox/gfx/matrix.Matrix2D |
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253 | }, |
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254 | invert: function(matrix){ |
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255 | // summary: |
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256 | // inverts a 2D matrix |
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257 | // matrix: dojox/gfx/matrix.Matrix2D |
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258 | // a 2D matrix-like object to be inverted |
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259 | // returns: dojox/gfx/matrix.Matrix2D |
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260 | var M = m.normalize(matrix), |
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261 | D = M.xx * M.yy - M.xy * M.yx; |
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262 | M = new m.Matrix2D({ |
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263 | xx: M.yy/D, xy: -M.xy/D, |
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264 | yx: -M.yx/D, yy: M.xx/D, |
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265 | dx: (M.xy * M.dy - M.yy * M.dx) / D, |
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266 | dy: (M.yx * M.dx - M.xx * M.dy) / D |
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267 | }); |
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268 | return M; // dojox/gfx/matrix.Matrix2D |
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269 | }, |
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270 | _multiplyPoint: function(matrix, x, y){ |
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271 | // summary: |
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272 | // applies a matrix to a point |
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273 | // matrix: dojox/gfx/matrix.Matrix2D |
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274 | // a 2D matrix object to be applied |
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275 | // x: Number |
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276 | // an x coordinate of a point |
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277 | // y: Number |
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278 | // a y coordinate of a point |
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279 | // returns: dojox/gfx.Point |
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280 | return {x: matrix.xx * x + matrix.xy * y + matrix.dx, y: matrix.yx * x + matrix.yy * y + matrix.dy}; // dojox/gfx.Point |
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281 | }, |
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282 | multiplyPoint: function(matrix, /* Number||Point */ a, /* Number? */ b){ |
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283 | // summary: |
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284 | // applies a matrix to a point |
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285 | // matrix: dojox/gfx/matrix.Matrix2D |
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286 | // a 2D matrix object to be applied |
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287 | // a: Number|dojox/gfx.Point |
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288 | // an x coordinate of a point, or a point |
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289 | // b: Number? |
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290 | // a y coordinate of a point |
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291 | // returns: dojox/gfx.Point |
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292 | var M = m.normalize(matrix); |
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293 | if(typeof a == "number" && typeof b == "number"){ |
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294 | return m._multiplyPoint(M, a, b); // dojox/gfx.Point |
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295 | } |
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296 | return m._multiplyPoint(M, a.x, a.y); // dojox/gfx.Point |
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297 | }, |
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298 | multiplyRectangle: function(matrix, /*Rectangle*/ rect){ |
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299 | // summary: |
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300 | // Applies a matrix to a rectangle. |
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301 | // description: |
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302 | // The method applies the transformation on all corners of the |
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303 | // rectangle and returns the smallest rectangle enclosing the 4 transformed |
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304 | // points. |
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305 | // matrix: dojox/gfx/matrix.Matrix2D |
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306 | // a 2D matrix object to be applied. |
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307 | // rect: Rectangle |
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308 | // the rectangle to transform. |
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309 | // returns: dojox/gfx.Rectangle |
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310 | var M = m.normalize(matrix); |
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311 | rect = rect || {x:0, y:0, width:0, height:0}; |
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312 | if(m.isIdentity(M)) |
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313 | return {x: rect.x, y: rect.y, width: rect.width, height: rect.height}; // dojo/gfx.Rectangle |
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314 | var p0 = m.multiplyPoint(M, rect.x, rect.y), |
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315 | p1 = m.multiplyPoint(M, rect.x, rect.y + rect.height), |
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316 | p2 = m.multiplyPoint(M, rect.x + rect.width, rect.y), |
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317 | p3 = m.multiplyPoint(M, rect.x + rect.width, rect.y + rect.height), |
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318 | minx = Math.min(p0.x, p1.x, p2.x, p3.x), |
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319 | miny = Math.min(p0.y, p1.y, p2.y, p3.y), |
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320 | maxx = Math.max(p0.x, p1.x, p2.x, p3.x), |
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321 | maxy = Math.max(p0.y, p1.y, p2.y, p3.y); |
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322 | return{ // dojo/gfx.Rectangle |
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323 | x: minx, |
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324 | y: miny, |
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325 | width: maxx - minx, |
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326 | height: maxy - miny |
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327 | }; |
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328 | }, |
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329 | multiply: function(matrix){ |
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330 | // summary: |
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331 | // combines matrices by multiplying them sequentially in the given order |
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332 | // matrix: dojox/gfx/matrix.Matrix2D |
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333 | // a 2D matrix-like object, |
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334 | // all subsequent arguments are matrix-like objects too |
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335 | var M = m.normalize(matrix); |
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336 | // combine matrices |
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337 | for(var i = 1; i < arguments.length; ++i){ |
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338 | var l = M, r = m.normalize(arguments[i]); |
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339 | M = new m.Matrix2D(); |
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340 | M.xx = l.xx * r.xx + l.xy * r.yx; |
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341 | M.xy = l.xx * r.xy + l.xy * r.yy; |
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342 | M.yx = l.yx * r.xx + l.yy * r.yx; |
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343 | M.yy = l.yx * r.xy + l.yy * r.yy; |
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344 | M.dx = l.xx * r.dx + l.xy * r.dy + l.dx; |
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345 | M.dy = l.yx * r.dx + l.yy * r.dy + l.dy; |
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346 | } |
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347 | return M; // dojox/gfx/matrix.Matrix2D |
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348 | }, |
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349 | |
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350 | // high level operations |
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351 | |
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352 | _sandwich: function(matrix, x, y){ |
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353 | // summary: |
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354 | // applies a matrix at a central point |
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355 | // matrix: dojox/gfx/matrix.Matrix2D |
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356 | // a 2D matrix-like object, which is applied at a central point |
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357 | // x: Number |
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358 | // an x component of the central point |
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359 | // y: Number |
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360 | // a y component of the central point |
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361 | return m.multiply(m.translate(x, y), matrix, m.translate(-x, -y)); // dojox/gfx/matrix.Matrix2D |
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362 | }, |
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363 | scaleAt: function(a, b, c, d){ |
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364 | // summary: |
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365 | // scales a picture using a specified point as a center of scaling |
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366 | // description: |
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367 | // Compare with dojox/gfx/matrix.scale(). |
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368 | // a: Number |
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369 | // a scaling factor used for the x coordinate, or a uniform scaling factor used for both coordinates |
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370 | // b: Number? |
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371 | // a scaling factor used for the y coordinate |
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372 | // c: Number|Point |
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373 | // an x component of a central point, or a central point |
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374 | // d: Number |
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375 | // a y component of a central point |
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376 | // returns: dojox/gfx/matrix.Matrix2D |
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377 | switch(arguments.length){ |
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378 | case 4: |
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379 | // a and b are scale factor components, c and d are components of a point |
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380 | return m._sandwich(m.scale(a, b), c, d); // dojox/gfx/matrix.Matrix2D |
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381 | case 3: |
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382 | if(typeof c == "number"){ |
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383 | return m._sandwich(m.scale(a), b, c); // dojox/gfx/matrix.Matrix2D |
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384 | } |
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385 | return m._sandwich(m.scale(a, b), c.x, c.y); // dojox/gfx/matrix.Matrix2D |
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386 | } |
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387 | return m._sandwich(m.scale(a), b.x, b.y); // dojox/gfx/matrix.Matrix2D |
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388 | }, |
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389 | rotateAt: function(angle, a, b){ |
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390 | // summary: |
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391 | // rotates a picture using a specified point as a center of rotation |
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392 | // description: |
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393 | // Compare with dojox/gfx/matrix.rotate(). |
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394 | // angle: Number |
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395 | // an angle of rotation in radians (>0 for CW) |
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396 | // a: Number|dojox/gfx.Point |
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397 | // an x component of a central point, or a central point |
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398 | // b: Number? |
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399 | // a y component of a central point |
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400 | // returns: dojox/gfx/matrix.Matrix2D |
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401 | if(arguments.length > 2){ |
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402 | return m._sandwich(m.rotate(angle), a, b); // dojox/gfx/matrix.Matrix2D |
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403 | } |
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404 | return m._sandwich(m.rotate(angle), a.x, a.y); // dojox/gfx/matrix.Matrix2D |
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405 | }, |
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406 | rotategAt: function(degree, a, b){ |
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407 | // summary: |
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408 | // rotates a picture using a specified point as a center of rotation |
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409 | // description: |
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410 | // Compare with dojox/gfx/matrix.rotateg(). |
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411 | // degree: Number |
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412 | // an angle of rotation in degrees (>0 for CW) |
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413 | // a: Number|dojox/gfx.Point |
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414 | // an x component of a central point, or a central point |
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415 | // b: Number? |
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416 | // a y component of a central point |
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417 | // returns: dojox/gfx/matrix.Matrix2D |
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418 | if(arguments.length > 2){ |
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419 | return m._sandwich(m.rotateg(degree), a, b); // dojox/gfx/matrix.Matrix2D |
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420 | } |
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421 | return m._sandwich(m.rotateg(degree), a.x, a.y); // dojox/gfx/matrix.Matrix2D |
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422 | }, |
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423 | skewXAt: function(angle, a, b){ |
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424 | // summary: |
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425 | // skews a picture along the x axis using a specified point as a center of skewing |
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426 | // description: |
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427 | // Compare with dojox/gfx/matrix.skewX(). |
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428 | // angle: Number |
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429 | // a skewing angle in radians |
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430 | // a: Number|dojox/gfx.Point |
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431 | // an x component of a central point, or a central point |
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432 | // b: Number? |
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433 | // a y component of a central point |
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434 | // returns: dojox/gfx/matrix.Matrix2D |
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435 | if(arguments.length > 2){ |
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436 | return m._sandwich(m.skewX(angle), a, b); // dojox/gfx/matrix.Matrix2D |
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437 | } |
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438 | return m._sandwich(m.skewX(angle), a.x, a.y); // dojox/gfx/matrix.Matrix2D |
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439 | }, |
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440 | skewXgAt: function(degree, a, b){ |
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441 | // summary: |
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442 | // skews a picture along the x axis using a specified point as a center of skewing |
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443 | // description: |
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444 | // Compare with dojox/gfx/matrix.skewXg(). |
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445 | // degree: Number |
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446 | // a skewing angle in degrees |
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447 | // a: Number|dojox/gfx.Point |
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448 | // an x component of a central point, or a central point |
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449 | // b: Number? |
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450 | // a y component of a central point |
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451 | // returns: dojox/gfx/matrix.Matrix2D |
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452 | if(arguments.length > 2){ |
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453 | return m._sandwich(m.skewXg(degree), a, b); // dojox/gfx/matrix.Matrix2D |
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454 | } |
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455 | return m._sandwich(m.skewXg(degree), a.x, a.y); // dojox/gfx/matrix.Matrix2D |
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456 | }, |
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457 | skewYAt: function(angle, a, b){ |
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458 | // summary: |
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459 | // skews a picture along the y axis using a specified point as a center of skewing |
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460 | // description: |
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461 | // Compare with dojox/gfx/matrix.skewY(). |
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462 | // angle: Number |
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463 | // a skewing angle in radians |
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464 | // a: Number|dojox/gfx.Point |
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465 | // an x component of a central point, or a central point |
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466 | // b: Number? |
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467 | // a y component of a central point |
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468 | // returns: dojox/gfx/matrix.Matrix2D |
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469 | if(arguments.length > 2){ |
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470 | return m._sandwich(m.skewY(angle), a, b); // dojox/gfx/matrix.Matrix2D |
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471 | } |
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472 | return m._sandwich(m.skewY(angle), a.x, a.y); // dojox/gfx/matrix.Matrix2D |
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473 | }, |
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474 | skewYgAt: function(/* Number */ degree, /* Number||Point */ a, /* Number? */ b){ |
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475 | // summary: |
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476 | // skews a picture along the y axis using a specified point as a center of skewing |
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477 | // description: |
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478 | // Compare with dojox/gfx/matrix.skewYg(). |
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479 | // degree: Number |
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480 | // a skewing angle in degrees |
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481 | // a: Number|dojox/gfx.Point |
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482 | // an x component of a central point, or a central point |
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483 | // b: Number? |
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484 | // a y component of a central point |
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485 | // returns: dojox/gfx/matrix.Matrix2D |
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486 | if(arguments.length > 2){ |
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487 | return m._sandwich(m.skewYg(degree), a, b); // dojox/gfx/matrix.Matrix2D |
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488 | } |
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489 | return m._sandwich(m.skewYg(degree), a.x, a.y); // dojox/gfx/matrix.Matrix2D |
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490 | } |
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491 | |
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492 | //TODO: rect-to-rect mapping, scale-to-fit (isotropic and anisotropic versions) |
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493 | |
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494 | }); |
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495 | // propagate Matrix2D up |
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496 | g.Matrix2D = m.Matrix2D; |
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497 | |
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498 | return m; |
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499 | }); |
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500 | |
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501 | |
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