Ratio interval half way 6.

docs/Basics/Stamp/Stamp.mdx

@@ -107,11 +107,11 @@ $L$ is the length of the current edge.
 By replacing $r(x)$, we get a quadratic equation $ax^2 + bx + c = 0$:
 
 $$
-\begin{align}
+\begin{aligned}
 a &= 1 - \cos^2\theta \\
-b &= - 2(r_0\cos\theta + x_p) \\
+b &= 2(r_0\cos\theta - x_p) \\
 c &= x_p^2 + y_p^2 - r_0^2
-\end{align}
+\end{aligned}
 $$
 
 Remind that $\cos\theta = (r_0 - r_1)/L$.

docs/Basics/Stamp/stampRound.frag

@@ -49,13 +49,14 @@ void main() {
     x2 = temp.y;
 
     // With the distance to the polyline's first vertex, we can compute a "stamp index" value.
-    // which indicate the number of stamp from the first vertex.
-    float index0 = l0/interval; // The stamp index of vertex0.
-    float startIndex, endIndex; // The stamp index's begin and end integral values
-    startIndex = x1 < 0.0 ? ceil(index0):ceil(index0 + x1/interval); // if x1 is less than zero, start the loop from vertex0.
+    // which indicate the number of stamp from the first vertex to current point.
+    float index0 = l0/interval; // The stamp index at vertex0.
+    float startIndex, endIndex; // The stamp index's begin and end values
+    float x1Index = index0 + x1/interval; // The stamp index at x1.
+    startIndex = x1 < 0.0 ? ceil(index0):ceil(x1Index); // if x1 is less than zero, start the loop from vertex0.
     float index1 = l1/interval;
-    float backIndex = x2/interval + index0;
-    endIndex = index1 < backIndex ? index1 : backIndex; // if x2 is larger than L, end the loop at vertex1.
+    float x2Index = x2/interval + index0;
+    endIndex = x2 > len ? index1 : x2Index; // if x2 is larger than L, end the loop at vertex1.
     if(startIndex > endIndex) discard;
 
     // The main loop to sample and blend color from the footprint, from `startIndex` to `endIndex`

docs/Introduction/Introduction.mdx

@@ -129,19 +129,6 @@ SIGGRAPH 2023 Talk
 }
 ```
 
-:::note Research Tip
-
-To demonstrate your research work about brush rendering, select vector drawings have variable radius or pen pressure data.
-Regular vector graphics datasets don't contain them.
-
-- OpenSketch: [Paper](https://dl.acm.org/doi/10.1145/3355089.3356533)
-- [Tracing versus freehand](https://zachzeyuwang.github.io/tracing-vs-freehand.html)
-- [DifferSketching](https://chufengxiao.github.io/DifferSketching/)
-- [Blender Grease Pencil](https://cloud.blender.org/p/gallery/5b642e25bf419c1042056fc6)
-- ... Tell me more in the [discussion](https://github.com/ShenCiao/brush-rendering-tutorial/discussions/1).
-
-:::
-
 [code repository]: https://github.com/ShenCiao/brush-rendering-tutorial
 [Ciallo]: https://github.com/ShenCiao/Ciallo
 [_The Book of Shader_]: https://thebookofshaders.com/