### Re: unit axis intercepts

I asked ChatGPT, because my brain exploded.

It sounds like you want to determine whether a line segment defined by two points {x1, y1} and {x2, y2} intersects the unit x and y axes, and if it does, where it intersects them. Additionally, you want to handle the special case where a segment from 0.1 to 1 on the axis is not considered an intercept, but 1 to 1.9 is. Here's a possible approach to solve this problem:

1. Calculate the intersection points of the line segment with the unit x and y axes.

To find the intersection points with the unit x-axis, you can use the equation of the line:

y = m * x + b

Where m is the slope of the line and b is the y-intercept. In your case, you can calculate the slope as:

m = (y2 - y1) / (x2 - x1)

Then, calculate the y-coordinate of the intersection point with the unit x-axis (where x = 0):

y_intersection_x = m * 0 + b = b

So, you have found the intersection point with the unit x-axis, which is {0, y_intersection_x}.

To find the intersection point with the unit y-axis, you can use the same equation with x = 1:

y_intersection_y = m * 1 + b

2. Check if the intersection points are within the desired range.

You mentioned that you want to consider an intercept only if it's within certain ranges. For the unit x-axis, you can check if the y-coordinate of the intersection point is within the range [0.1, 1.9]. For the unit y-axis, you can check if the y-coordinate of the intersection point is within the range [0.1, 1.9].

Here's some Python-like pseudocode to implement this:

``````python
# Calculate the slope of the line
m = (y2 - y1) / (x2 - x1)

# Calculate the y-intercept
b = y1 - m * x1

# Calculate the intersection point with the unit x-axis
y_intersection_x = b

# Calculate the intersection point with the unit y-axis
y_intersection_y = m * 1 + b

# Check if the intersections are within the desired range
if 0.1 <= y_intersection_x <= 1.9:
# Intersection with unit x-axis is within the desired range
hitux = True
else:
hitux = False

if 0.1 <= y_intersection_y <= 1.9:
# Intersection with unit y-axis is within the desired range
hituy = True
else:
hituy = False

```
```

This code should help you determine whether the line segment intersects the unit x and y axes within the specified ranges. If it does, the `hitux` and `hituy` variables will be set to True, indicating an intersection, and you can also retrieve the intersection points if needed.

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