55 * Since the {@code ColorModel} and {@code Raster} classes
56 * allow the storage of pixel data in either premultiplied or
57 * non-premultiplied form, all input data must be normalized into
58 * premultiplied form before applying the equations and all results
59 * might need to be adjusted back to the form required by the destination
60 * before the pixel values are stored.
61 *
62 * <p>
63 * Also note that this class defines only the equations
64 * for combining color and alpha values in a purely mathematical
65 * sense. The accurate application of its equations depends
66 * on the way the data is retrieved from its sources and stored
67 * in its destinations.
68 * See <a href="#caveats">Implementation Caveats</a>
69 * for further information.
70 *
71 * <p>
72 * The following factors are used in the description of the blending
73 * equation in the Porter and Duff paper:
74 *
75 * <blockquote>
76 * <table class="borderless">
77 * <caption style="display:none">Factors</caption>
78 * <tr><th style="text-align:left">Factor <th style="text-align:left">Definition
79 * <tr><td><em>A<sub>s</sub></em><td>the alpha component of the source pixel
80 * <tr><td><em>C<sub>s</sub></em><td>a color component of the source pixel in premultiplied form
81 * <tr><td><em>A<sub>d</sub></em><td>the alpha component of the destination pixel
82 * <tr><td><em>C<sub>d</sub></em><td>a color component of the destination pixel in premultiplied form
83 * <tr><td><em>F<sub>s</sub></em><td>the fraction of the source pixel that contributes to the output
84 * <tr><td><em>F<sub>d</sub></em><td>the fraction of the destination pixel that contributes
85 * to the output
86 * <tr><td><em>A<sub>r</sub></em><td>the alpha component of the result
87 * <tr><td><em>C<sub>r</sub></em><td>a color component of the result in premultiplied form
88 * </table>
89 * </blockquote>
90 *
91 * <p>
92 * Using these factors, Porter and Duff define 12 ways of choosing
93 * the blending factors <em>F<sub>s</sub></em> and <em>F<sub>d</sub></em> to
94 * produce each of 12 desirable visual effects.
95 * The equations for determining <em>F<sub>s</sub></em> and <em>F<sub>d</sub></em>
96 * are given in the descriptions of the 12 static fields
97 * that specify visual effects.
98 * For example,
99 * the description for
100 * <a href="#SRC_OVER">{@code SRC_OVER}</a>
101 * specifies that <em>F<sub>s</sub></em> = 1 and <em>F<sub>d</sub></em> = (1-<em>A<sub>s</sub></em>).
102 * Once a set of equations for determining the blending factors is
103 * known they can then be applied to each pixel to produce a result
104 * using the following set of equations:
105 *
106 * <pre>
107 * <em>F<sub>s</sub></em> = <em>f</em>(<em>A<sub>d</sub></em>)
108 * <em>F<sub>d</sub></em> = <em>f</em>(<em>A<sub>s</sub></em>)
109 * <em>A<sub>r</sub></em> = <em>A<sub>s</sub></em>*<em>F<sub>s</sub></em> + <em>A<sub>d</sub></em>*<em>F<sub>d</sub></em>
110 * <em>C<sub>r</sub></em> = <em>C<sub>s</sub></em>*<em>F<sub>s</sub></em> + <em>C<sub>d</sub></em>*<em>F<sub>d</sub></em></pre>
111 *
112 * <p>
113 * The following factors will be used to discuss our extensions to
114 * the blending equation in the Porter and Duff paper:
115 *
116 * <blockquote>
117 * <table class="borderless">
118 * <caption style="display:none">Factors</caption>
119 * <tr><th style="text-align:left">Factor <th style="text-align:left">Definition
120 * <tr><td><em>C<sub>sr</sub></em> <td>one of the raw color components of the source pixel
121 * <tr><td><em>C<sub>dr</sub></em> <td>one of the raw color components of the destination pixel
122 * <tr><td><em>A<sub>ac</sub></em> <td>the "extra" alpha component from the AlphaComposite instance
123 * <tr><td><em>A<sub>sr</sub></em> <td>the raw alpha component of the source pixel
124 * <tr><td><em>A<sub>dr</sub></em><td>the raw alpha component of the destination pixel
125 * <tr><td><em>A<sub>df</sub></em> <td>the final alpha component stored in the destination
126 * <tr><td><em>C<sub>df</sub></em> <td>the final raw color component stored in the destination
127 * </table>
128 *</blockquote>
129 *
130 * <h3>Preparing Inputs</h3>
131 *
132 * <p>
133 * The {@code AlphaComposite} class defines an additional alpha
134 * value that is applied to the source alpha.
135 * This value is applied as if an implicit SRC_IN rule were first
136 * applied to the source pixel against a pixel with the indicated
137 * alpha by multiplying both the raw source alpha and the raw
138 * source colors by the alpha in the {@code AlphaComposite}.
139 * This leads to the following equation for producing the alpha
140 * used in the Porter and Duff blending equation:
141 *
142 * <pre>
143 * <em>A<sub>s</sub></em> = <em>A<sub>sr</sub></em> * <em>A<sub>ac</sub></em> </pre>
144 *
145 * All of the raw source color components need to be multiplied
146 * by the alpha in the {@code AlphaComposite} instance.
147 * Additionally, if the source was not in premultiplied form
148 * then the color components also need to be multiplied by the
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55 * Since the {@code ColorModel} and {@code Raster} classes
56 * allow the storage of pixel data in either premultiplied or
57 * non-premultiplied form, all input data must be normalized into
58 * premultiplied form before applying the equations and all results
59 * might need to be adjusted back to the form required by the destination
60 * before the pixel values are stored.
61 *
62 * <p>
63 * Also note that this class defines only the equations
64 * for combining color and alpha values in a purely mathematical
65 * sense. The accurate application of its equations depends
66 * on the way the data is retrieved from its sources and stored
67 * in its destinations.
68 * See <a href="#caveats">Implementation Caveats</a>
69 * for further information.
70 *
71 * <p>
72 * The following factors are used in the description of the blending
73 * equation in the Porter and Duff paper:
74 *
75 * <table class="striped">
76 * <caption style="display:none">Factors</caption>
77 * <thead>
78 * <tr>
79 * <th scope="col">Factor
80 * <th scope="col">Definition
81 * </thead>
82 * <tbody>
83 * <tr>
84 * <th scope="row"><em>A<sub>s</sub></em>
85 * <td>the alpha component of the source pixel
86 * <tr>
87 * <th scope="row"><em>C<sub>s</sub></em>
88 * <td>a color component of the source pixel in premultiplied form
89 * <tr>
90 * <th scope="row"><em>A<sub>d</sub></em>
91 * <td>the alpha component of the destination pixel
92 * <tr>
93 * <th scope="row"><em>C<sub>d</sub></em>
94 * <td>a color component of the destination pixel in premultiplied form
95 * <tr>
96 * <th scope="row"><em>F<sub>s</sub></em>
97 * <td>the fraction of the source pixel that contributes to the output
98 * <tr>
99 * <th scope="row"><em>F<sub>d</sub></em>
100 * <td>the fraction of the destination pixel that contributes to the output
101 * <tr>
102 * <th scope="row"><em>A<sub>r</sub></em>
103 * <td>the alpha component of the result
104 * <tr>
105 * <th scope="row"><em>C<sub>r</sub></em>
106 * <td>a color component of the result in premultiplied form
107 * </tbody>
108 * </table>
109 * <p>
110 * Using these factors, Porter and Duff define 12 ways of choosing
111 * the blending factors <em>F<sub>s</sub></em> and <em>F<sub>d</sub></em> to
112 * produce each of 12 desirable visual effects.
113 * The equations for determining <em>F<sub>s</sub></em> and <em>F<sub>d</sub></em>
114 * are given in the descriptions of the 12 static fields
115 * that specify visual effects.
116 * For example,
117 * the description for
118 * <a href="#SRC_OVER">{@code SRC_OVER}</a>
119 * specifies that <em>F<sub>s</sub></em> = 1 and <em>F<sub>d</sub></em> = (1-<em>A<sub>s</sub></em>).
120 * Once a set of equations for determining the blending factors is
121 * known they can then be applied to each pixel to produce a result
122 * using the following set of equations:
123 *
124 * <pre>
125 * <em>F<sub>s</sub></em> = <em>f</em>(<em>A<sub>d</sub></em>)
126 * <em>F<sub>d</sub></em> = <em>f</em>(<em>A<sub>s</sub></em>)
127 * <em>A<sub>r</sub></em> = <em>A<sub>s</sub></em>*<em>F<sub>s</sub></em> + <em>A<sub>d</sub></em>*<em>F<sub>d</sub></em>
128 * <em>C<sub>r</sub></em> = <em>C<sub>s</sub></em>*<em>F<sub>s</sub></em> + <em>C<sub>d</sub></em>*<em>F<sub>d</sub></em></pre>
129 *
130 * <p>
131 * The following factors will be used to discuss our extensions to
132 * the blending equation in the Porter and Duff paper:
133 *
134 * <table class="striped">
135 * <caption style="display:none">Factors</caption>
136 * <thead>
137 * <tr>
138 * <th scope="col">Factor
139 * <th scope="col">Definition
140 * </thead>
141 * <tbody>
142 * <tr>
143 * <th scope="row"><em>C<sub>sr</sub></em>
144 * <td>one of the raw color components of the source pixel
145 * <tr>
146 * <th scope="row"><em>C<sub>dr</sub></em>
147 * <td>one of the raw color components of the destination pixel
148 * <tr>
149 * <th scope="row"><em>A<sub>ac</sub></em>
150 * <td>the "extra" alpha component from the AlphaComposite instance
151 * <tr>
152 * <th scope="row"><em>A<sub>sr</sub></em>
153 * <td>the raw alpha component of the source pixel
154 * <tr>
155 * <th scope="row"><em>A<sub>dr</sub></em>
156 * <td>the raw alpha component of the destination pixel
157 * <tr>
158 * <th scope="row"><em>A<sub>df</sub></em>
159 * <td>the final alpha component stored in the destination
160 * <tr>
161 * <th scope="row"><em>C<sub>df</sub></em>
162 * <td>the final raw color component stored in the destination
163 * </tbody>
164 * </table>
165 *
166 * <h3>Preparing Inputs</h3>
167 *
168 * <p>
169 * The {@code AlphaComposite} class defines an additional alpha
170 * value that is applied to the source alpha.
171 * This value is applied as if an implicit SRC_IN rule were first
172 * applied to the source pixel against a pixel with the indicated
173 * alpha by multiplying both the raw source alpha and the raw
174 * source colors by the alpha in the {@code AlphaComposite}.
175 * This leads to the following equation for producing the alpha
176 * used in the Porter and Duff blending equation:
177 *
178 * <pre>
179 * <em>A<sub>s</sub></em> = <em>A<sub>sr</sub></em> * <em>A<sub>ac</sub></em> </pre>
180 *
181 * All of the raw source color components need to be multiplied
182 * by the alpha in the {@code AlphaComposite} instance.
183 * Additionally, if the source was not in premultiplied form
184 * then the color components also need to be multiplied by the
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