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heliannuuthusheliannuuthus
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optimize markmap
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‎blog/2025-04/_partials/calculus.mdx‎

Lines changed: 43 additions & 43 deletions
Original file line numberDiff line numberDiff line change
@@ -110,8 +110,8 @@ A_{11} & \cdots & A_{1n} \\ \vdots & \ddots & \vdots \\ A_{m1} & \cdots & A_{mn}
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\end{bmatrix}$"}：
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<Collapse label="$$
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\nabla_x (A x) = A^T
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$$">
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\nabla_x (A x) = A^T
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$$">
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$$
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\begin{split}
@@ -136,23 +136,23 @@ A_{11} & \cdots & A_{1m} \\ \vdots & \ddots & \vdots \\ A_{n1} & \cdots & A_{nm}
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\end{bmatrix}$"}：
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<Collapse label="$$
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\nabla_x (x^T A) = A
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$$">
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$$
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\begin{split}
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&\ \nabla_x (x^T A) = \nabla_x (x_1 A_1 + x_2 A_2 + \cdots + x_n A_n) \\
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=&\ \nabla_x (x_1 [A_{11} \cdots A_{1m}] + x_2 [A_{21} \cdots A_{2m}] + \cdots + x_n [A_{n1} \cdots A_{nm}]) \\
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=&\ \nabla_x (x_1 A_1 + x_2 A_2 + \cdots + x_n A_n) \\
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=&\ \nabla_x (x_1 A_1) + \nabla_x (x_2 A_2) + \cdots + \nabla_x (x_n A_n) \\
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=&\ \begin{bmatrix} \
149-
\frac{\partial}{\partial x_1} (x_1 A_1) , \frac{\partial}{\partial x_2} (x_2 A_2) , \cdots , \frac{\partial}{\partial x_n} (x_n A_n)
150-
\end{bmatrix} \\
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=&\ \begin{bmatrix}
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A_1 , A_2 , \cdots , A_n
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\end{bmatrix} = A
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\end{split}
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$$
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\nabla_x (x^T A) = A
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$$">
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$$
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\begin{split}
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&\ \nabla_x (x^T A) = \nabla_x (x_1 A_1 + x_2 A_2 + \cdots + x_n A_n) \\
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=&\ \nabla_x (x_1 [A_{11} \cdots A_{1m}] + x_2 [A_{21} \cdots A_{2m}] + \cdots + x_n [A_{n1} \cdots A_{nm}]) \\
146+
=&\ \nabla_x (x_1 A_1 + x_2 A_2 + \cdots + x_n A_n) \\
147+
=&\ \nabla_x (x_1 A_1) + \nabla_x (x_2 A_2) + \cdots + \nabla_x (x_n A_n) \\
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=&\ \begin{bmatrix} \
149+
\frac{\partial}{\partial x_1} (x_1 A_1) , \frac{\partial}{\partial x_2} (x_2 A_2) , \cdots , \frac{\partial}{\partial x_n} (x_n A_n)
150+
\end{bmatrix} \\
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=&\ \begin{bmatrix}
152+
A_1 , A_2 , \cdots , A_n
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\end{bmatrix} = A
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\end{split}
155+
$$
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</Collapse>
158158

@@ -164,20 +164,20 @@ A_{11} & \cdots & A_{1n} \\ \vdots & \ddots & \vdots \\ A_{n1} & \cdots & A_{nn}
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\end{bmatrix}$"}：
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<Collapse label="$$
167-
\nabla_x x^T A x = (A + A^T) x
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$$">
169-
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$$
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\begin{split}
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&\ \nabla_x x^T A x = \nabla_x \sum_{i=1}^n \sum_{j=1}^n x_i A_{ij} x_j \\
173-
=&\ \frac{\partial}{\partial x_k} \sum_{i=1}^n \sum_{j=1}^n x_i A_{ij} x_j + \frac{\partial}{\partial x_k} \sum_{i=1}^n \sum_{j=1}^n x_j A_{ji} x_i \\
174-
=&\ \sum_{i=1}^n \sum_{j=1}^n A_{ij} x_j + \sum_{i=1}^n \sum_{j=1}^n A_{ji} x_i \\
175-
=&\ \sum_{j=1}^n A_{kj} x_j + \sum_{i=1}^n A_{ik} x_i \text{（$i, j = k$ 时，$A_{kj} x_j, A_{ik} x_i$ 分别存在一项 $A_{kk} x_k$）} \\
176-
=&\ \sum_{i=1}^n (\sum_{j=1}^n A_{ij} x_j) \cdot e_i + \sum_{j=1}^n (\sum_{i=1}^n A_{ji} x_i) \cdot e_j \\
177-
=&\ \sum_{i=1}^n (\mathbf{A} \mathbf{x})_i \cdot e_i + \sum_{j=1}^n (\mathbf{A^T} \mathbf{x})_j \cdot e_j \\ \
178-
=&\ (A + A^T) x
179-
\end{split}
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$$
167+
\nabla_x x^T A x = (A + A^T) x
168+
$$">
169+
170+
$$
171+
\begin{split}
172+
&\ \nabla_x x^T A x = \nabla_x \sum_{i=1}^n \sum_{j=1}^n x_i A_{ij} x_j \\
173+
=&\ \frac{\partial}{\partial x_k} \sum_{i=1}^n \sum_{j=1}^n x_i A_{ij} x_j + \frac{\partial}{\partial x_k} \sum_{i=1}^n \sum_{j=1}^n x_j A_{ji} x_i \\
174+
=&\ \sum_{i=1}^n \sum_{j=1}^n A_{ij} x_j + \sum_{i=1}^n \sum_{j=1}^n A_{ji} x_i \\
175+
=&\ \sum_{j=1}^n A_{kj} x_j + \sum_{i=1}^n A_{ik} x_i \text{（$i, j = k$ 时，$A_{kj} x_j, A_{ik} x_i$ 分别存在一项 $A_{kk} x_k$）} \\
176+
=&\ \sum_{i=1}^n (\sum_{j=1}^n A_{ij} x_j) \cdot e_i + \sum_{j=1}^n (\sum_{i=1}^n A_{ji} x_i) \cdot e_j \\
177+
=&\ \sum_{i=1}^n (\mathbf{A} \mathbf{x})_i \cdot e_i + \sum_{j=1}^n (\mathbf{A^T} \mathbf{x})_j \cdot e_j \\ \
178+
=&\ (A + A^T) x
179+
\end{split}
180+
$$
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</Collapse>
183183

@@ -196,16 +196,16 @@ A_{11} & \cdots & A_{1n} \\ \vdots & \ddots & \vdots \\ A_{n1} & \cdots & A_{nn}
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\end{bmatrix}$"}：
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<Collapse label="$$
199-
\nabla_x \|x\|_2^2 = \nabla_x (x^T x) = 2x
200-
$$">
201-
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$$
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\begin{split}
204-
&\ \nabla_x \|x\|_2 = \nabla_x (\sqrt{x^T x}) ^ 2 \\
205-
=&\ \nabla_x (x^T x) = \nabla_x (x_1^2 + x_2^2 + \cdots + x_n^2) \\
206-
=&\ 2x
207-
\end{split}
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$$
199+
\nabla_x \|x\|_2^2 = \nabla_x (x^T x) = 2x
200+
$$">
201+
202+
$$
203+
\begin{split}
204+
&\ \nabla_x \|x\|_2 = \nabla_x (\sqrt{x^T x}) ^ 2 \\
205+
=&\ \nabla_x (x^T x) = \nabla_x (x_1^2 + x_2^2 + \cdots + x_n^2) \\
206+
=&\ 2x
207+
\end{split}
208+
$$
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</Collapse>
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‎package.json‎

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@@ -43,6 +43,7 @@
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"canvas": "^3.1.0",
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"canvg": "^4.0.2",
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"clsx": "^2.0.0",
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"d3": "^7.9.0",
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"echarts": "^5.5.1",
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"file-saver": "^2.0.5",
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"heliannuuthus-docusaurus-authors": "file:./plugins/docusaurus-authors",
@@ -88,6 +89,7 @@
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"@docusaurus/tsconfig": "3.8.1",
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"@docusaurus/types": "3.8.1",
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"@trivago/prettier-plugin-sort-imports": "^5.2.0",
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"@types/d3": "^7.4.3",
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"@types/file-saver": "^2.0.7",
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"@types/react": "^19.0.0",
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"@types/react-dom": "^19.0.0",

‎pnpm-lock.yaml‎

Lines changed: 6 additions & 0 deletions
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‎src/components/markdown/markmap/context.ts‎

Lines changed: 26 additions & 14 deletions
Original file line numberDiff line numberDiff line change
@@ -63,8 +63,9 @@ export const transformPath = (svg: markmap.ID3SVGElement) => {
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const cyCollections = new Map<string, number>();
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svg
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.node()
66-
.querySelectorAll("g")
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?.querySelectorAll(".markmap-node")
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.forEach((g: SVGGElement) => {
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console.log(g);
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const dataPath = g.getAttribute("data-path");
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const circle = g.querySelector("circle");
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if (circle && dataPath) {
@@ -89,21 +90,32 @@ export const transformPath = (svg: markmap.ID3SVGElement) => {
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}
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svg
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.node()
92-
?.querySelectorAll("path")
93+
?.querySelectorAll(".markmap-link")
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.forEach((path: SVGPathElement) => {
95+
console.log(path);
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const dataPath = path.getAttribute("data-path");
95-
if (dataPath) {
96-
const parentPath = dataPath.split(".").slice(0, -1).join(".");
97-
const parsed = path.getPathData();
98-
for (const seg of parsed) {
99-
const argc = seg.values.length;
100-
if (argc >= 2) {
101-
for (let i = 1; i < argc; i += 2) {
102-
seg.values[i] =
103-
Number(seg.values[i]) - cyCollections.get(parentPath);
104-
}
105-
}
106-
}
97+
if (!dataPath) return;
98+
const parentPath = dataPath.split(".").slice(0, -1).join(".");
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const parentCy = cyCollections.get(parentPath) ?? 0;
100+
const currentCy = cyCollections.get(dataPath) ?? parentCy;
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const parsed = path.getPathData();
102+
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if (
104+
parsed &&
105+
parsed.length >= 2 &&
106+
parsed[0].type === "M" &&
107+
parsed[1].type === "C"
108+
) {
109+
parsed[0].values[1] -= parentCy;
110+
parsed[1].values[5] -= currentCy;
111+
112+
const offset = currentCy - parentCy;
113+
const c1 = 1 / 3;
114+
const c2 = 2 / 3;
115+
116+
parsed[1].values[1] -= parentCy + offset * c1;
117+
parsed[1].values[3] -= parentCy + offset * c2;
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const result = parsed
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.map((seg) => seg.type + seg.values.join(","))
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.join("");

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