{"topic":{"id":13654,"title":"关于物理模拟部分 (实验 2.13-2.15 文档) 描述的疑问","slug":"topic","categoryId":56,"createdAt":"2024-10-07 04:34:53.327473","bumpedAt":"2024-10-17 09:59:24.476306","views":390,"postsCount":6,"highestPostNumber":6,"likeCount":3,"closed":false,"pinned":false,"pinnedGlobally":false,"pinnedAt":null,"pinnedUntil":null,"isBanner":false,"excerpt":"在实验 2.13 的实验指导书中: 如果在此基础上进一步实现了前向欧拉法，那么你可以再获得 2 分，共计 10 分。该实验的分数共计是否应为 5 分？在实验 2.14 的实验指导书中：如果你试着修改实验 2.12 中... 2024fall 的实验指导书中实验 2.12 是实现一个拉普拉斯平滑算法，这里是否指的是实验 2.13，也就是 2024fall 物理模拟部分的第一个实验理论上当方块重新落回水平面时应该在 (4, 0,…","deletedAt":null,"isAnonymous":false,"category":{"id":56,"name":"计算机图形学","slug":"cg","color":"92278F"},"author":{"id":201,"username":"rouge","name":null,"avatarUrl":"/uploads/image/05/fa/05fa884d60107653efc49f1e94c3aea99a31315428bb1562339968bbd19266ff.avif"},"tags":[]},"posts":[{"id":41329,"postNumber":1,"raw":"## 在实验 2.13 的实验指导书中:\n![image about lab2.13|690x78](/uploads/image/4f/bb/4fbb4aa68498997752b5d5d9689bd6d538c422535fd73b397902461c77dab640.avif)\n1. > 如果在此基础上进一步实现了前向欧拉法，那么你可以再获得 2 分，共计 10 分。\n\n 该实验的分数共计是否应为 5 分？\n\n## 在实验 2.14 的实验指导书中：\n![image about Lab2.14|690x78](/uploads/image/a0/52/a0526cbc67619db12d55b7aea698d45775911d6d0057a3579c9bfc8396654739.avif)\n\n2. >如果你试着修改实验 2.12 中...\n \n [2024fall 的实验指导书](https://xjtu.app/t/topic/13473) 中实验 2.12 是实现一个拉普拉斯平滑算法，这里是否指的是实验 2.13，也就是 2024fall 物理模拟部分的第一个实验\n3. > 理论上当方块重新落回水平面时应该在 (4, 0, 0) 处，实际上会偏离大约 0.2 格\n\n 根据前向欧拉法以及这里的运动学模型，我的理解是：\n $$\n\\begin{array}{c}\n \\left.\\begin{matrix} \n \\frac{\\text{d}\\textbf{x}}{\\text{d}t} & = & f_1(t, \\textbf{x}) & = & \\textbf{v}\\\\\n \\frac{\\text{d}\\textbf{v}}{\\text{d}t} & = & f_2(t, \\textbf{v}) & = & \\textbf{a}\\\\\n \\textbf{a} & \\equiv &\\textbf{F}/m\n\\end{matrix} \\right\\}\n&\\Rightarrow&\n\\left\\{\n\\begin{array}{l}\nf_1(t, \\textbf{x}) = t\\cdot \\textbf{a} + \\textbf{v}_0\\\\ \n\\textbf{x}_{n+1} = \\textbf{x}_{n}+\\Delta t\\cdot f_1(t_{n}, \\textbf{x}_{n})\n\\end{array}\n\\right.\n\\\\\n \\quad &\\Rightarrow& \\textbf{x}_{n} = \\textbf{x}_{0}+t\\textbf{v}_0 +\\Delta t \\sum\\limits_{i=1}^{n-1}t_i \\cdot \\textbf{a}\n\\\\\n \\quad &\\Rightarrow& \\textbf{x}_{n} = \\textbf{x}_0 + n\\Delta t\\textbf{v}_0 +\\frac{n(n-1)}{2} {\\Delta t}^2\\textbf{a}\n\\end{array}\n $$\n 那么可以在 $y$ 方向上解得重新落回水平面时 $n=21$ . 将 $n=21$ 代入 $x$ 方向得到此时的 $x$ 应为 $4.4$. 这样一来误差似乎大约为 $0.4$ 格 :thinking:\n## 在实验 2.15 的实验指导书中\n![image about lab2.15|690x114](/uploads/image/a3/fa/a3fa860e01fce62c432e163e571419007d31a13ee3c240b407bb00f4c3cf7f68.avif)\n\n4. > 关于射线求交的算法请参考 Whitted-Style Ray-Tracing（实验 2.4）的文档。\n\n [2024fall 的文档](https://xjtu.app/t/topic/13473) 中实验 Whitted-Style Ray-Tracing 的编号为 2.6。**同时结合上面的反馈 2，是物理模拟部分的实验编号的错误还是文档中所引用实验编号的错误 :technologist:**","cooked":"

在实验 2.13 的实验指导书中:

$\"image$

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如果在此基础上进一步实现了前向欧拉法，那么你可以再获得 2 分，共计 10 分。
\n
\n
该实验的分数共计是否应为 5 分？
\n

在实验 2.14 的实验指导书中：

$\"image$

\n
\n
如果你试着修改实验 2.12 中...
\n
\n
2024fall 的实验指导书中实验 2.12 是实现一个拉普拉斯平滑算法，这里是否指的是实验 2.13，也就是 2024fall 物理模拟部分的第一个实验
\n
\n
\n
理论上当方块重新落回水平面时应该在 (4, 0, 0) 处，实际上会偏离大约 0.2 格
\n
\n
根据前向欧拉法以及这里的运动学模型，我的理解是：
\n
$\n\\begin{array}{c}\n\\left.\\begin{matrix} \n\\frac{\\text{d}\\textbf{x}}{\\text{d}t} & = & f_1(t, \\textbf{x}) & = & \\textbf{v}\\\\\n\\frac{\\text{d}\\textbf{v}}{\\text{d}t} & = & f_2(t, \\textbf{v}) & = & \\textbf{a}\\\\\n\\textbf{a} & \\equiv &\\textbf{F}/m\n\\end{matrix} \\right\\}\n&\\Rightarrow&\n\\left\\{\n\\begin{array}{l}\nf_1(t, \\textbf{x}) = t\\cdot \\textbf{a} + \\textbf{v}_0\\\\ \n\\textbf{x}_{n+1} = \\textbf{x}_{n}+\\Delta t\\cdot f_1(t_{n}, \\textbf{x}_{n})\n\\end{array}\n\\right.\n\\\\\n\\quad &\\Rightarrow& \\textbf{x}_{n} = \\textbf{x}_{0}+t\\textbf{v}_0 +\\Delta t \\sum\\limits_{i=1}^{n-1}t_i \\cdot \\textbf{a}\n\\\\\n\\quad &\\Rightarrow& \\textbf{x}_{n} = \\textbf{x}_0 + n\\Delta t\\textbf{v}_0 +\\frac{n(n-1)}{2} {\\Delta t}^2\\textbf{a}\n\\end{array}\n$

\n那么可以在 $y$ 方向上解得重新落回水平面时 $n=21$ . 将 $n=21$ 代入 $x$ 方向得到此时的 $x$ 应为 $4.4$ . 这样一来误差似乎大约为 $0.4$ 格 🤔
\n

在实验 2.15 的实验指导书中

$\"image$

\n
\n
关于射线求交的算法请参考 Whitted-Style Ray-Tracing（实验 2.4）的文档。
\n
\n
2024fall 的文档中实验 Whitted-Style Ray-Tracing 的编号为 2.6。同时结合上面的反馈 2，是物理模拟部分的实验编号的错误还是文档中所引用实验编号的错误 🧑‍💻
\n

\n","createdAt":"2024-10-07 04:34:53.579531","updatedAt":"2024-10-08 06:04:47.822276","replyToPostNumber":null,"replyCount":0,"likeCount":3,"wordCount":426,"liked":false,"bookmarked":false,"polls":[],"reactions":[{"reaction":"❤️","count":2,"users":[{"id":4053,"username":"nayC","name":"Cyan Chen"},{"id":4668,"username":"IO","name":null}],"hasReacted":false}],"wiki":false,"version":2,"publicVersion":2,"deletedAt":null,"isAnonymous":false,"user":{"id":201,"username":"rouge","name":null,"avatarUrl":"/uploads/image/05/fa/05fa884d60107653efc49f1e94c3aea99a31315428bb1562339968bbd19266ff.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":41429,"postNumber":2,"raw":"点了，同问","cooked":"

点了，同问

\n","createdAt":"2024-10-08 15:40:31.189288","updatedAt":"2024-10-08 15:40:31.189288","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":5,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":4053,"username":"nayC","name":"Cyan Chen","avatarUrl":"/uploads/image/e9/22/e922488de19153fd560c5629e04ffa7209febce78f4fd37c1f1cb51d86c48dee.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":41450,"postNumber":3,"raw":"先回答一下编号的问题，物理模拟部分是我们的编号没更新过来。感谢指出，相关的编号我们后续更正。","cooked":"

先回答一下编号的问题，物理模拟部分是我们的编号没更新过来。感谢指出，相关的编号我们后续更正。

\n","createdAt":"2024-10-09 08:53:31.843676","updatedAt":"2024-10-09 08:53:31.843676","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":46,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":1381,"username":"greyishsong","name":"greyishsong","avatarUrl":"/uploads/image/da/bc/dabc731b0311f59850625bbeb55ed969fcfac0430c5ef0f68441e5466b7aa496.avif","admin":false,"moderator":true,"signatureRaw":null,"signatureCooked":null}},{"id":41460,"postNumber":4,"raw":"第三个问题，误差是 0.4 格，我们后续会更新文档，感谢指正。","cooked":"

第三个问题，误差是 0.4 格，我们后续会更新文档，感谢指正。

\n","createdAt":"2024-10-09 13:30:11.191232","updatedAt":"2024-10-09 13:30:11.191232","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":27,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":6031,"username":"wangying","name":"wangying","avatarUrl":null,"admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":41475,"postNumber":5,"raw":"感谢回复😊","cooked":"

感谢回复😊

\n","createdAt":"2024-10-10 10:37:51.899321","updatedAt":"2024-10-10 10:37:51.899321","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":5,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":201,"username":"rouge","name":null,"avatarUrl":"/uploads/image/05/fa/05fa884d60107653efc49f1e94c3aea99a31315428bb1562339968bbd19266ff.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":41727,"postNumber":6,"raw":"实验 2.14 中，按我对后向欧拉法和半隐式欧拉法的理解，这里加速度恒定的前提下，实现是一致的，并且仍然会产生 0.4 格偏移，不过偏移方向和前向欧拉法相反，请问我的理解正确吗？","cooked":"

实验 2.14 中，按我对后向欧拉法和半隐式欧拉法的理解，这里加速度恒定的前提下，实现是一致的，并且仍然会产生 0.4 格偏移，不过偏移方向和前向欧拉法相反，请问我的理解正确吗？

\n","createdAt":"2024-10-17 09:59:24.476306","updatedAt":"2024-10-17 09:59:24.476306","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":80,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":1202,"username":"shinnrryuu","name":"神竜","avatarUrl":"/uploads/image/bc/31/bc31850c60444497d7b0f17ffcdc4665bc4f1cdebdce58efd973839de6349398.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}}],"hasMore":false,"lastReadPostNumber":6,"hasUrlPostNumber":true}