how to draw angle (d theta) between two curve lines?

Bonjour ,

une solution avec Point on Object

or

Maybe you are looking for angle between the tangents

improved (see al1T)

l1 and l2 are lists based on command Sequence()

Note: <variable i> is an arbitrary (local) name that exists only within (this) Sequence(). This name is used in <expression> to modify the <expression> for each list item. In this example the RigthSide of the equation.

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l3 generates a list of all intersections of l1 and l2. This happens in a nested Sequence(Sequence())

The outer Sequence() traverses the (integer) indices of l1 and returns this index named "m" to the <expression> of the inner Sequence() (it could also be the <expression> of the outer sequence (), but that is not needed here).

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The <expression> of the outer Sequence() is also a Sequence() and is called as inner sequence. The inner Sequence() traverses the (integer) indices of l2 and returns this index named "n" to the <expression> of the inner Sequence(). This creates one element in the list l3 for each conceivable combination of l1 and l2 (respectively m and n).

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Flatten() causes the curly braces of the inner lists to be resolved, resulting in a simple (one-dimensional) list (instead of a matrix). Depending on the equations used, it is conceivable that an intersection point was generated twice. Unique() removes these duplicate list items.

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Tangent looks exotic. This is because there is a GGB-bug (wrong syntax-error) in the context of If(RightSide(<equ>)==0, Line(), Tangent())

The Problem: a tangent to a line (index==11 in l1 and l2) is not possible, the result is undefined. Both possibilities (tangent and line) are created in a list and undefined are deleted and only the first element is used.

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Your points 2 and 3 are realized in the attachment. The left part of the equation is created as text. Note the script in eql1 and eql2, which transform this text into an expression, which are used in l1 and l2.