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貝茲曲線 - 修訂歷史
2026-04-09T22:50:29Z
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丁志仁 於 2024年8月1日 (四) 16:36
2024-08-01T16:36:25Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2024年8月1日 (四) 16:36 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >第1行：</td>
<td colspan="2" class="diff-lineno">第1行：</td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[分類:數學]][[分類:<del class="diffchange diffchange-inline">HTML</del>]]</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[分類:數學]][[分類:<ins class="diffchange diffchange-inline">SVG</ins>]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==一次貝茲曲線==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==一次貝茲曲線==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><div style='float:right'><img src='https://upload.wikimedia.org/wikipedia/commons/0/00/B%C3%A9zier_1_big.gif'/></div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><div style='float:right'><img src='https://upload.wikimedia.org/wikipedia/commons/0/00/B%C3%A9zier_1_big.gif'/></div></div></td></tr>
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丁志仁
http://jendo.synology.me/wiki1231/index.php?title=%E8%B2%9D%E8%8C%B2%E6%9B%B2%E7%B7%9A&diff=59201&oldid=prev
丁志仁：/* (一)先求兩控制點與最低點的 y 值關係 */
2023-10-03T09:22:42Z
<p><span dir="auto"><span class="autocomment">(一)先求兩控制點與最低點的 y 值關係</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2023年10月3日 (二) 09:22 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l133" >第133行：</td>
<td colspan="2" class="diff-lineno">第133行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&ensp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>1</sub><sup>2</sup>-3h<sub>1</sub><sup>2</sup>+3h<sub>1</sub>h<sub>2</sub></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&ensp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>1</sub><sup>2</sup>-3h<sub>1</sub><sup>2</sup>+3h<sub>1</sub>h<sub>2</sub></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&ensp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>1</sub><sup>2</sup>-h<sub>1</sub>h<sub>2</sub>+h<sub>2</sub><sup>2</sup></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&ensp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>1</sub><sup>2</sup>-h<sub>1</sub>h<sub>2</sub>+h<sub>2</sub><sup>2</sup></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">====(二)特殊解：求兩控制點等高時====</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">若 h<sub>1</sub>＝h<sub>2</sub>＝h</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">:B<sub>y</sub>′(t)＝3[h＋2(-h)t]＝0</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">:h＋2(-h)t＝0 => h=2ht => t=½</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">B<sub>y</sub>(½)＝3[½h-¼h]＝¾h</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==參考文章==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==參考文章==</div></td></tr>
</table>
丁志仁
http://jendo.synology.me/wiki1231/index.php?title=%E8%B2%9D%E8%8C%B2%E6%9B%B2%E7%B7%9A&diff=59200&oldid=prev
丁志仁：/* (一)先求兩控制點與最低點的 y 值關係 */
2023-10-03T09:09:22Z
<p><span dir="auto"><span class="autocomment">(一)先求兩控制點與最低點的 y 值關係</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2023年10月3日 (二) 09:09 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l132" >第132行：</td>
<td colspan="2" class="diff-lineno">第132行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t＝[2(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span>] / 2×3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t＝[2(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span>] / 2×3(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&ensp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>1</sub><sup>2</sup>-3h<sub>1</sub><sup>2</sup>+3h<sub>1</sub>h<sub>2</sub></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&ensp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>1</sub><sup>2</sup>-3h<sub>1</sub><sup>2</sup>+3h<sub>1</sub>h<sub>2</sub></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:&ensp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>1</sub><del class="diffchange diffchange-inline">h</del><<del class="diffchange diffchange-inline">sub</del>>2</<del class="diffchange diffchange-inline">sub</del>>-h<sub>1</sub>h<sub>2</sub>+h<sub><del class="diffchange diffchange-inline">1</del></sub><sup>2</sup></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:&ensp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>1</sub><<ins class="diffchange diffchange-inline">sup</ins>>2</<ins class="diffchange diffchange-inline">sup</ins>>-h<sub>1</sub>h<sub>2</sub>+h<sub><ins class="diffchange diffchange-inline">2</ins></sub><sup>2</sup></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==參考文章==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==參考文章==</div></td></tr>
</table>
丁志仁
http://jendo.synology.me/wiki1231/index.php?title=%E8%B2%9D%E8%8C%B2%E6%9B%B2%E7%B7%9A&diff=59199&oldid=prev
丁志仁：/* (一)先求兩控制點與最低點的 y 值關係 */
2023-10-03T09:08:06Z
<p><span dir="auto"><span class="autocomment">(一)先求兩控制點與最低點的 y 值關係</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2023年10月3日 (二) 09:08 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l132" >第132行：</td>
<td colspan="2" class="diff-lineno">第132行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t＝[2(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span>] / 2×3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t＝[2(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span>] / 2×3(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&ensp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>1</sub><sup>2</sup>-3h<sub>1</sub><sup>2</sup>+3h<sub>1</sub>h<sub>2</sub></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&ensp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>1</sub><sup>2</sup>-3h<sub>1</sub><sup>2</sup>+3h<sub>1</sub>h<sub>2</sub></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<del class="diffchange diffchange-inline">t=</del><<del class="diffchange diffchange-inline">span style='font</del>-<del class="diffchange diffchange-inline">stretch:condensed;'</del>><del class="diffchange diffchange-inline">½</del></<del class="diffchange diffchange-inline">span</del>></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<ins class="diffchange diffchange-inline">&ensp;＝[(2h<sub>1</ins><<ins class="diffchange diffchange-inline">/sub></ins>-<ins class="diffchange diffchange-inline">h<sub</ins>><ins class="diffchange diffchange-inline">2</ins></<ins class="diffchange diffchange-inline">sub</ins>><ins class="diffchange diffchange-inline">)±√</ins><span <ins class="diffchange diffchange-inline">class</ins>='<ins class="diffchange diffchange-inline">overline</ins>-<ins class="diffchange diffchange-inline">segment</ins>'><ins class="diffchange diffchange-inline">h<sub>1</ins></<ins class="diffchange diffchange-inline">sub</ins>><ins class="diffchange diffchange-inline">h</ins><sub><ins class="diffchange diffchange-inline">2</ins></sub><ins class="diffchange diffchange-inline">-h</ins><sub><ins class="diffchange diffchange-inline">1</ins></sub><ins class="diffchange diffchange-inline">h</ins><<ins class="diffchange diffchange-inline">sub</ins>><ins class="diffchange diffchange-inline">2</ins></<ins class="diffchange diffchange-inline">sub</ins>><ins class="diffchange diffchange-inline">+h</ins><<ins class="diffchange diffchange-inline">sub</ins>><ins class="diffchange diffchange-inline">1</ins></<ins class="diffchange diffchange-inline">sub><sup</ins>><ins class="diffchange diffchange-inline">2</ins><<ins class="diffchange diffchange-inline">/sup</ins>></span><ins class="diffchange diffchange-inline">] / 3(h</ins><<ins class="diffchange diffchange-inline">sub</ins>><ins class="diffchange diffchange-inline">1</ins></<ins class="diffchange diffchange-inline">sub</ins>><ins class="diffchange diffchange-inline">-h</ins><<ins class="diffchange diffchange-inline">sub</ins>><ins class="diffchange diffchange-inline">2</ins></<ins class="diffchange diffchange-inline">sub</ins>><ins class="diffchange diffchange-inline">)</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">將 t=</del><span <del class="diffchange diffchange-inline">style</del>='<del class="diffchange diffchange-inline">font</del>-<del class="diffchange diffchange-inline">stretch:condensed;</del>'><del class="diffchange diffchange-inline">½ </del></<del class="diffchange diffchange-inline">span</del>><del class="diffchange diffchange-inline">代入 B</del><sub><del class="diffchange diffchange-inline">y</del></sub><del class="diffchange diffchange-inline">(t) ，我們得到：</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:B</del><sub><del class="diffchange diffchange-inline">y</del></sub><del class="diffchange diffchange-inline">(</del><<del class="diffchange diffchange-inline">span style='font-stretch:condensed;'</del>><del class="diffchange diffchange-inline">½</del></<del class="diffchange diffchange-inline">span</del>><del class="diffchange diffchange-inline">)=2β(</del><<del class="diffchange diffchange-inline">span style='font-stretch:condensed;'</del>><del class="diffchange diffchange-inline">½</del></<del class="diffchange diffchange-inline">span</del>><del class="diffchange diffchange-inline">)(</del><<del class="diffchange diffchange-inline">span style='font-stretch:condensed;'</del>><del class="diffchange diffchange-inline">½</del></span><del class="diffchange diffchange-inline">)=</del><<del class="diffchange diffchange-inline">span style='font-stretch:condensed;'</del>><del class="diffchange diffchange-inline">½ </del></<del class="diffchange diffchange-inline">span</del>><del class="diffchange diffchange-inline">β</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">因此，最低點的 y 值是 </del><<del class="diffchange diffchange-inline">span style='font-stretch:condensed;'</del>><del class="diffchange diffchange-inline">½ </del></<del class="diffchange diffchange-inline">span</del>><del class="diffchange diffchange-inline">β 。</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==參考文章==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==參考文章==</div></td></tr>
</table>
丁志仁
http://jendo.synology.me/wiki1231/index.php?title=%E8%B2%9D%E8%8C%B2%E6%9B%B2%E7%B7%9A&diff=59198&oldid=prev
丁志仁：/* (一)先求兩控制點與最低點的 y 值關係 */
2023-10-03T09:03:02Z
<p><span dir="auto"><span class="autocomment">(一)先求兩控制點與最低點的 y 值關係</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2023年10月3日 (二) 09:03 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l131" >第131行：</td>
<td colspan="2" class="diff-lineno">第131行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將斜率設為 0 以解 t：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將斜率設為 0 以解 t：</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t＝[2(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span>] / 2×3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t＝[2(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span>] / 2×3(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:&ensp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub><del class="diffchange diffchange-inline">2</del></sub><sup>2</sup>-3h<sub>1</sub><sup>2</sup>+3h<sub>1</sub>h<sub>2</sub></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:&ensp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub><ins class="diffchange diffchange-inline">1</ins></sub><sup>2</sup>-3h<sub>1</sub><sup>2</sup>+3h<sub>1</sub>h<sub>2</sub></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t=<span style='font-stretch:condensed;'>½</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t=<span style='font-stretch:condensed;'>½</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將 t=<span style='font-stretch:condensed;'>½ </span>代入 B<sub>y</sub>(t) ，我們得到：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將 t=<span style='font-stretch:condensed;'>½ </span>代入 B<sub>y</sub>(t) ，我們得到：</div></td></tr>
</table>
丁志仁
http://jendo.synology.me/wiki1231/index.php?title=%E8%B2%9D%E8%8C%B2%E6%9B%B2%E7%B7%9A&diff=59197&oldid=prev
丁志仁：/* (一)先求兩控制點與最低點的 y 值關係 */
2023-10-03T09:01:16Z
<p><span dir="auto"><span class="autocomment">(一)先求兩控制點與最低點的 y 值關係</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2023年10月3日 (二) 09:01 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l131" >第131行：</td>
<td colspan="2" class="diff-lineno">第131行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將斜率設為 0 以解 t：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將斜率設為 0 以解 t：</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t＝[2(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span>] / 2×3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t＝[2(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span>] / 2×3(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:&<del class="diffchange diffchange-inline">emsp</del>;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>-3h<sub>1</sub><del class="diffchange diffchange-inline">-h</del><<del class="diffchange diffchange-inline">sub</del>>2</<del class="diffchange diffchange-inline">sub</del>>+3h<sub>1</sub>h<sub>2</sub></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:&<ins class="diffchange diffchange-inline">ensp</ins>;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>-3h<sub>1</sub><<ins class="diffchange diffchange-inline">sup</ins>>2</<ins class="diffchange diffchange-inline">sup</ins>>+3h<sub>1</sub>h<sub>2</sub></span>] / 3(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t=<span style='font-stretch:condensed;'>½</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t=<span style='font-stretch:condensed;'>½</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將 t=<span style='font-stretch:condensed;'>½ </span>代入 B<sub>y</sub>(t) ，我們得到：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將 t=<span style='font-stretch:condensed;'>½ </span>代入 B<sub>y</sub>(t) ，我們得到：</div></td></tr>
</table>
丁志仁
http://jendo.synology.me/wiki1231/index.php?title=%E8%B2%9D%E8%8C%B2%E6%9B%B2%E7%B7%9A&diff=59196&oldid=prev
丁志仁：/* (一)先求兩控制點與最低點的 y 值關係 */
2023-10-03T08:58:09Z
<p><span dir="auto"><span class="autocomment">(一)先求兩控制點與最低點的 y 值關係</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2023年10月3日 (二) 08:58 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l130" >第130行：</td>
<td colspan="2" class="diff-lineno">第130行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:B<sub>y</sub>′(t)＝3[h<sub>1</sub>＋2(h<sub>2</sub>-2h<sub>1</sub>)t＋3(h<sub>1</sub>-h<sub>2</sub>)t<sup>2</sup>]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:B<sub>y</sub>′(t)＝3[h<sub>1</sub>＋2(h<sub>2</sub>-2h<sub>1</sub>)t＋3(h<sub>1</sub>-h<sub>2</sub>)t<sup>2</sup>]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將斜率設為 0 以解 t：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將斜率設為 0 以解 t：</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:t＝[2(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span> / 2×3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:t＝[2(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span><ins class="diffchange diffchange-inline">] </ins>/ 2×3<ins class="diffchange diffchange-inline">(h<sub>1</sub>-h<sub>2</sub>)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:&emsp;＝[(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+4h<sub>2</sub><sup>2</sup>-3h<sub>1</sub>-h<sub>2</sub>+3h<sub>1</sub>h<sub>2</sub></span>] / 3</ins>(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t=<span style='font-stretch:condensed;'>½</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t=<span style='font-stretch:condensed;'>½</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將 t=<span style='font-stretch:condensed;'>½ </span>代入 B<sub>y</sub>(t) ，我們得到：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將 t=<span style='font-stretch:condensed;'>½ </span>代入 B<sub>y</sub>(t) ，我們得到：</div></td></tr>
</table>
丁志仁
http://jendo.synology.me/wiki1231/index.php?title=%E8%B2%9D%E8%8C%B2%E6%9B%B2%E7%B7%9A&diff=59195&oldid=prev
丁志仁：/* (一)先求兩控制點與最低點的 y 值關係 */
2023-10-03T08:51:48Z
<p><span dir="auto"><span class="autocomment">(一)先求兩控制點與最低點的 y 值關係</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2023年10月3日 (二) 08:51 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l130" >第130行：</td>
<td colspan="2" class="diff-lineno">第130行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:B<sub>y</sub>′(t)＝3[h<sub>1</sub>＋2(h<sub>2</sub>-2h<sub>1</sub>)t＋3(h<sub>1</sub>-h<sub>2</sub>)t<sup>2</sup>]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:B<sub>y</sub>′(t)＝3[h<sub>1</sub>＋2(h<sub>2</sub>-2h<sub>1</sub>)t＋3(h<sub>1</sub>-h<sub>2</sub>)t<sup>2</sup>]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將斜率設為 0 以解 t：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將斜率設為 0 以解 t：</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<del class="diffchange diffchange-inline">t＝2</del>(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+<del class="diffchange diffchange-inline">h</del><sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span> / 2×3(h<sub>1</sub>-h<sub>2</sub>)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<ins class="diffchange diffchange-inline">t＝[2</ins>(2h<sub>1</sub>-h<sub>2</sub>)±√<span class='overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+<ins class="diffchange diffchange-inline">4h</ins><sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span> / 2×3(h<sub>1</sub>-h<sub>2</sub>)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t=<span style='font-stretch:condensed;'>½</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t=<span style='font-stretch:condensed;'>½</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將 t=<span style='font-stretch:condensed;'>½ </span>代入 B<sub>y</sub>(t) ，我們得到：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將 t=<span style='font-stretch:condensed;'>½ </span>代入 B<sub>y</sub>(t) ，我們得到：</div></td></tr>
<!-- diff cache key wiki1231:diff::1.12:old-59194:rev-59195 -->
</table>
丁志仁
http://jendo.synology.me/wiki1231/index.php?title=%E8%B2%9D%E8%8C%B2%E6%9B%B2%E7%B7%9A&diff=59194&oldid=prev
丁志仁：/* (一)先求兩控制點與最低點的 y 值關係 */
2023-10-03T08:50:18Z
<p><span dir="auto"><span class="autocomment">(一)先求兩控制點與最低點的 y 值關係</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2023年10月3日 (二) 08:50 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l128" >第128行：</td>
<td colspan="2" class="diff-lineno">第128行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&emsp;＝3×t(1−t)[h<sub>1</sub>＋(h<sub>2</sub>−h<sub>1</sub>)t]＝3×[h<sub>1</sub>t＋(h<sub>2</sub>−2h<sub>1</sub>)t<sup>2</sup>＋(h<sub>1</sub>−h<sub>2</sub>)t<sup>3</sup>]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&emsp;＝3×t(1−t)[h<sub>1</sub>＋(h<sub>2</sub>−h<sub>1</sub>)t]＝3×[h<sub>1</sub>t＋(h<sub>2</sub>−2h<sub>1</sub>)t<sup>2</sup>＋(h<sub>1</sub>−h<sub>2</sub>)t<sup>3</sup>]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>對其進行微分：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>對其進行微分：</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:B<sub>y</sub>′(t)<del class="diffchange diffchange-inline">=3</del>[h<sub>1</sub>＋2(h<sub>2</sub>-2h<sub>1</sub>)t＋3(h<sub>1</sub>-h<sub>2</sub>)t<sup>2</sup>]</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:B<sub>y</sub>′(t)<ins class="diffchange diffchange-inline">＝3</ins>[h<sub>1</sub>＋2(h<sub>2</sub>-2h<sub>1</sub>)t＋3(h<sub>1</sub>-h<sub>2</sub>)t<sup>2</sup>]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將斜率設為 0 以解 t：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將斜率設為 0 以解 t：</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<del class="diffchange diffchange-inline">1−2t</del>=<del class="diffchange diffchange-inline">0</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<ins class="diffchange diffchange-inline">t＝2(2h<sub>1</sub>-h<sub>2</sub>)±√<span class</ins>=<ins class="diffchange diffchange-inline">'overline-segment'>4(h<sub>2</sub><sup>2</sup>-4h<sub>1</sub>h<sub>2</sub>+h<sub>2</sub><sup>2</sup>)-4×3(h<sub>1</sub>-h<sub>2</sub>)h<sub>1</sub></span> / 2×3(h<sub>1</sub>-h<sub>2</sub>)</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t=<span style='font-stretch:condensed;'>½</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t=<span style='font-stretch:condensed;'>½</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將 t=<span style='font-stretch:condensed;'>½ </span>代入 B<sub>y</sub>(t) ，我們得到：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將 t=<span style='font-stretch:condensed;'>½ </span>代入 B<sub>y</sub>(t) ，我們得到：</div></td></tr>
</table>
丁志仁
http://jendo.synology.me/wiki1231/index.php?title=%E8%B2%9D%E8%8C%B2%E6%9B%B2%E7%B7%9A&diff=59191&oldid=prev
丁志仁：/* (一)先求兩控制點與最低點的 y 值關係 */
2023-10-03T08:24:58Z
<p><span dir="auto"><span class="autocomment">(一)先求兩控制點與最低點的 y 值關係</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2023年10月3日 (二) 08:24 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l125" >第125行：</td>
<td colspan="2" class="diff-lineno">第125行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====(一)先求兩控制點與最低點的 y 值關係====</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====(一)先求兩控制點與最低點的 y 值關係====</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將控制點的 y 值代入 B<sub>y</sub>(t) 的方程式，我們得到：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>將控制點的 y 值代入 B<sub>y</sub>(t) 的方程式，我們得到：</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:B<sub>y</sub>(t)＝(1−t)<sup>3</sup>×0＋3(1−t)<sup>2</sup>t×h<sub>1</sub>＋3(1−t)t<sup>2</sup>×h<sub>2</sub>＋t<sup>3</sup>×0＝3×t(1−t)[h<sub>1</sub>-h<sub>1</sub>t+h<sub>2</sub>t]＝3×t(1−t)[h<sub>1</sub><del class="diffchange diffchange-inline">+</del>(h<sub>2</sub><del class="diffchange diffchange-inline">-h</del><sub>1</sub>)t]</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:B<sub>y</sub>(t)＝(1−t)<sup>3</sup>×0＋3(1−t)<sup>2</sup>t×h<sub>1</sub>＋3(1−t)t<sup>2</sup>×h<sub>2</sub>＋t<sup>3</sup>×0＝3×t(1−t)[h<sub>1</sub>-h<sub>1</sub>t+h<sub>2</sub>t]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:&emsp;</del>＝3×[h<sub>1</sub>t＋(h<sub>2</sub><del class="diffchange diffchange-inline">-2h</del><sub>1</sub>)t<sup>2</sup>＋(h<sub>1</sub><del class="diffchange diffchange-inline">-h</del><sub>2</sub>)t<sup>3</sup>]</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:&emsp;</ins>＝3×t(1−t)[h<sub>1</sub><ins class="diffchange diffchange-inline">＋</ins>(h<sub>2</sub><ins class="diffchange diffchange-inline">−h</ins><sub>1</sub>)t]＝3×[h<sub>1</sub>t＋(h<sub>2</sub><ins class="diffchange diffchange-inline">−2h</ins><sub>1</sub>)t<sup>2</sup>＋(h<sub>1</sub><ins class="diffchange diffchange-inline">−h</ins><sub>2</sub>)t<sup>3</sup>]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>對其進行微分：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>對其進行微分：</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:B<sub>y</sub>′(t)=3[h<sub>1</sub>＋2(h<sub>2</sub>-2h<sub>1</sub>)t＋3(h<sub>1</sub>-h<sub>2</sub>)t<sup>2</sup>]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:B<sub>y</sub>′(t)=3[h<sub>1</sub>＋2(h<sub>2</sub>-2h<sub>1</sub>)t＋3(h<sub>1</sub>-h<sub>2</sub>)t<sup>2</sup>]</div></td></tr>
</table>
丁志仁