I believe that Hermite splines also have additional parameters such as tension, bias, and continuity. Tension controls how rigid the curve is. From the previous slide where it showed a curved wooden stick, the tension parameter essentially models how bendable the stick is. Bias controls the symmetry of the curve. A negative bias may pull the curve towards one point and a positive bias may pull it towards the other, kind of like gravity. Lastly, continuity models how fast or sharp the curve can bend, which essentially describes the maximum angle at which the line can change directions at.
nickjiang2378
This is another good resource for hermite interpolations - goes through some examples. https://coast.nd.edu/jjwteach/www/www/60130/New%20Lecture%20Notes_PDF/CE60130_Lecture%208%20with_footer-v04.pdf
S-Muddana
You make a good point about Hermite splines. By adjusting those parameters judiciously, Hermite splines offer a powerful tool for curve interpolation that can adapt to a wide range of design requirements and artistic preferences, allowing for precise control over the resulting curve's shape, smoothness, and overall aesthetic appeal.
s3kim2018
This is connected off of a discussion question, but could we use any derivative pairs to successfully interpolate a, b, c, and d for a cubic polynomial?
Other than have to calculate the second derivate and its points, is there any consequence to using P(0), P(1), P''(0), P'''(1)?
I believe that Hermite splines also have additional parameters such as tension, bias, and continuity. Tension controls how rigid the curve is. From the previous slide where it showed a curved wooden stick, the tension parameter essentially models how bendable the stick is. Bias controls the symmetry of the curve. A negative bias may pull the curve towards one point and a positive bias may pull it towards the other, kind of like gravity. Lastly, continuity models how fast or sharp the curve can bend, which essentially describes the maximum angle at which the line can change directions at.
This is another good resource for hermite interpolations - goes through some examples. https://coast.nd.edu/jjwteach/www/www/60130/New%20Lecture%20Notes_PDF/CE60130_Lecture%208%20with_footer-v04.pdf
You make a good point about Hermite splines. By adjusting those parameters judiciously, Hermite splines offer a powerful tool for curve interpolation that can adapt to a wide range of design requirements and artistic preferences, allowing for precise control over the resulting curve's shape, smoothness, and overall aesthetic appeal.
This is connected off of a discussion question, but could we use any derivative pairs to successfully interpolate a, b, c, and d for a cubic polynomial? Other than have to calculate the second derivate and its points, is there any consequence to using P(0), P(1), P''(0), P'''(1)?