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The Path API in Android supports Bézier curves, which are a little different than Hermite curves regarding parameters. Fortunately Hermite curves can be converted to Bézier curves. Here is the first example code I found when Googling. This Stackoverflow answer also seems to give the formula.

Based on this answer, the intersection point can be calculated with the following formula:

Edit3: As it seems to be hard to get good input values for the curve generation, I propose another approach: Use serialization. Android Path doesn't seem to support it, but fortunately Region class does. See this answer for the code. This should give you the exact result. It might take some space in the serialized form if it's not optimized, but in that case it should compress very well. Compression is easy in Android Java using GZIPOutputStream.

The Path API in Android supports Bézier curves, which are a little different than Hermite curves regarding parameters. Fortunately Hermite curves can be converted to Bézier curves. Here is the first example code I found when Googling. This Stackoverflow answer also seems to give the formula.

Based on this answer, the intersection point can be calculated with the following formula:

Edit3: As it seems to be hard to get good input values for the curve generation, I propose another approach: Use serialization. Android Path doesn't seem to support it, but fortunately Region class does. See this answer for the code. This should give you the exact result. It might take some space in the serialized form if it's not optimized, but in that case it should compress very well. Compression is easy in Android Java using GZIPOutputStream.

Edit3: As it seems to be hard to get good input values for the curve generation, I propose another approach: Use serialization. Android Path doesn't seem to support it, but fortunately Region class does. See this answer for the code. This should give you the exact result. It might take some space in the serialized form if it's not optimized, but in that case it should compress very well. Compression is easy in Android Java using GZIPOutputStream.

Edit2: If your drawing position is in p1, you can calculate the bezier control points to p2 with the following pseudo code:

vec2 p0, p1, p2, p3; // These are calculated with PathMeasure
vec2 cp1 = p1 + (p2 - p0) / 6;
vec2 cp2 = p2 - (p3 - p1) / 6;

With these you can append a path from p1 to p2:

path.cubicTo(cp1.x, cp1.y, cp2.x, cp2.y, p2.x, p2.y);

Replace the vector operations with per component operations on float[2] arrays to match your code. You start by initializing p1 = start; and p2 and p3 are the next points. p0 is initially undefined. For the first segment where you don't have p0 yet, you can use a quadratic curve from p1 to p2 with cp2 as the control point. The same for the end of the path where you don't have p3, you can draw a quadratic curve from p1 to p2 with cp1 as the control point. Alternatively you can initialize p0=p1 for the first segment and p3=p2 for the last segment. After every segment you shift the values p0 = p1; p1 = p2; and p2 = p3; when moving forward.

When you are saving the path, you just save all points p0 ... pN. No need to save the control points cp1 and cp2, as they can be calculated as needed.