### Re: unit axis intercepts

- Posted by ChrisB (moderator) in September
- 746 views

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.