prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  Options of `point` argument
  Documentation of `point` argument in marks isn't very easily discoverable.
  
  Recently I tried to create a chart with colored line and points. My first try was with `mark_line(color="red", point=True)`, similarly to [this example](https://altair-viz.github.io/gallery/line_chart_with_points.html), but it produced red line with blue points. This turned out to be current default behavior of Vega-lite (found in [this issue](https://github.com/vega/vega-lite/issues/6111)).
  
  After some digging, I found that `point` can be "an object defining the properties of the overlayed points." (which seems to imply `OverlayMarkDef`, but simple dictionary showed to be enough). I think it would be really helpful to have this slightly easier to find. A "Line chart with points" example seems like a good place.
  
  So, what do you think about adding some sort of variation of the following code snippet in that example?
  ```python
  import altair as alt
  import numpy as np
  import pandas as pd
  
  x = np.arange(100)
  source = pd.DataFrame({"x": x, "f(x)": np.sin(x / 5)})
  
  # Only this part will be added
  alt.Chart(source).mark_line(
      color="red", point={"color": "red"}
  ).encode(
      x="x",
      y="f(x)"
  )
  ```
  ![issue_altair_point-argument_example](https://user-images.githubusercontent.com/24854248/79694414-c5890880-8278-11ea-884b-ab9d4969b717.png)
  
  If this is OK, I would like to help with PR. Thanks.
  
  </issue>
  <code>
  [start of altair/examples/line_chart_with_points.py]
  1 """
  2 Line Chart with Points
  3 ----------------------
  4 This chart shows a simple line chart with points marking each value.
  5 """
  6 # category: line charts
  7 import altair as alt
  8 import numpy as np
  9 import pandas as pd
  10 
  11 x = np.arange(100)
  12 source = pd.DataFrame({
  13   'x': x,
  14   'f(x)': np.sin(x / 5)
  15 })
  16 
  17 alt.Chart(source).mark_line(point=True).encode(
  18     x='x',
  19     y='f(x)'
  20 )
  21
  [end of altair/examples/line_chart_with_points.py]
  </code>
  
  I need you to solve this issue by generating a single patch file that I can apply directly to this repository using git apply. Please respond with a single patch file in the following format.
  <patch>
  diff --git a/file.py b/file.py
  --- a/file.py
  +++ b/file.py
  @@ -1,27 +1,35 @@
   def euclidean(a, b):
  -    while b:
  -        a, b = b, a % b
  -    return a
  +    if b == 0:
  +        return a
  +    return euclidean(b, a % b)
   
   
   def bresenham(x0, y0, x1, y1):
       points = []
       dx = abs(x1 - x0)
       dy = abs(y1 - y0)
  -    sx = 1 if x0 < x1 else -1
  -    sy = 1 if y0 < y1 else -1
  -    err = dx - dy
  +    x, y = x0, y0
  +    sx = -1 if x0 > x1 else 1
  +    sy = -1 if y0 > y1 else 1
   
  -    while True:
  -        points.append((x0, y0))
  -        if x0 == x1 and y0 == y1:
  -            break
  -        e2 = 2 * err
  -        if e2 > -dy:
  -            err -= dy
  -            x0 += sx
  -        if e2 < dx:
  -            err += dx
  -            y0 += sy
  +    if dx > dy:
  +        err = dx / 2.0
  +        while x != x1:
  +            points.append((x, y))
  +            err -= dy
  +            if err < 0:
  +                y += sy
  +                err += dx
  +            x += sx
  +    else:
  +        err = dy / 2.0
  +        while y != y1:
  +            points.append((x, y))
  +            err -= dx
  +            if err < 0:
  +                x += sx
  +                err += dy
  +            y += sy
  +
  +    points.append((x, y))
       return points
  
  </patch>
golden_diff: diff --git a/altair/examples/line_chart_with_points.py b/altair/examples/line_chart_with_points.py
  --- a/altair/examples/line_chart_with_points.py
  +++ b/altair/examples/line_chart_with_points.py
  @@ -1,7 +1,9 @@
   """
   Line Chart with Points
   ----------------------
  -This chart shows a simple line chart with points marking each value.
  +This chart shows a simple line chart with points marking each value. Use
  +``point=True`` for points with default appearance or customize it with
  +``OverlayMarkDef()``.
   """
   # category: line charts
   import altair as alt
  @@ -14,7 +16,9 @@
     'f(x)': np.sin(x / 5)
   })
   
  -alt.Chart(source).mark_line(point=True).encode(
  +alt.Chart(source).mark_line(
  +    point=alt.OverlayMarkDef(color="red")
  +).encode(
       x='x',
       y='f(x)'
   )
  
verification_info: {"golden_diff": "diff --git a/altair/examples/line_chart_with_points.py b/altair/examples/line_chart_with_points.py\n--- a/altair/examples/line_chart_with_points.py\n+++ b/altair/examples/line_chart_with_points.py\n@@ -1,7 +1,9 @@\n \"\"\"\n Line Chart with Points\n ----------------------\n-This chart shows a simple line chart with points marking each value.\n+This chart shows a simple line chart with points marking each value. Use\n+``point=True`` for points with default appearance or customize it with\n+``OverlayMarkDef()``.\n \"\"\"\n # category: line charts\n import altair as alt\n@@ -14,7 +16,9 @@\n   'f(x)': np.sin(x / 5)\n })\n \n-alt.Chart(source).mark_line(point=True).encode(\n+alt.Chart(source).mark_line(\n+    point=alt.OverlayMarkDef(color=\"red\")\n+).encode(\n     x='x',\n     y='f(x)'\n )\n", "issue": "Options of `point` argument\nDocumentation of `point` argument in marks isn't very easily discoverable.\r\n\r\nRecently I tried to create a chart with colored line and points. My first try was with `mark_line(color=\"red\", point=True)`, similarly to [this example](https://altair-viz.github.io/gallery/line_chart_with_points.html), but it produced red line with blue points. This turned out to be current default behavior of Vega-lite (found in [this issue](https://github.com/vega/vega-lite/issues/6111)).\r\n\r\nAfter some digging, I found that `point` can be \"an object defining the properties of the overlayed points.\" (which seems to imply `OverlayMarkDef`, but simple dictionary showed to be enough). I think it would be really helpful to have this slightly easier to find. A \"Line chart with points\" example seems like a good place.\r\n\r\nSo, what do you think about adding some sort of variation of the following code snippet in that example?\r\n```python\r\nimport altair as alt\r\nimport numpy as np\r\nimport pandas as pd\r\n\r\nx = np.arange(100)\r\nsource = pd.DataFrame({\"x\": x, \"f(x)\": np.sin(x / 5)})\r\n\r\n# Only this part will be added\r\nalt.Chart(source).mark_line(\r\n    color=\"red\", point={\"color\": \"red\"}\r\n).encode(\r\n    x=\"x\",\r\n    y=\"f(x)\"\r\n)\r\n```\r\n![issue_altair_point-argument_example](https://user-images.githubusercontent.com/24854248/79694414-c5890880-8278-11ea-884b-ab9d4969b717.png)\r\n\r\nIf this is OK, I would like to help with PR. Thanks.\n", "before_files": [{"content": "\"\"\"\nLine Chart with Points\n----------------------\nThis chart shows a simple line chart with points marking each value.\n\"\"\"\n# category: line charts\nimport altair as alt\nimport numpy as np\nimport pandas as pd\n\nx = np.arange(100)\nsource = pd.DataFrame({\n  'x': x,\n  'f(x)': np.sin(x / 5)\n})\n\nalt.Chart(source).mark_line(point=True).encode(\n    x='x',\n    y='f(x)'\n)\n", "path": "altair/examples/line_chart_with_points.py"}]}