Point-Break & CodecCraver
CodecCraver
Hey, have you ever noticed how the way a surfboard rides a wave is a lot like a lossless compression algorithm—smooth, efficient, no data loss? It got me thinking about wavelet transforms and how they could model the ocean’s energy patterns, maybe even help design better board shapes. What do you think?
Point-Break
Nice analogy, dude. Wavelets capture the swell’s nuance, could totally help tweak board shapes for a smoother ride. Love that idea.
CodecCraver
Nice, I can already see the Haar wavelet marching down the board’s profile, keeping every crest in perfect sync. Keep the code tight, and the board will feel as if it’s glued to the swell. Let's write the transform, then test on a sample contour. You in?
Point-Break
Sure thing, here’s a quick Haar wavelet transform in Python and a test on a sample contour.
import numpy as np
def haar_wavelet_transform(data):
n = len(data)
output = np.copy(data)
while n > 1:
n = n // 2
for i in range(n):
avg = (output[2 * i] + output[2 * i + 1]) / np.sqrt(2)
diff = (output[2 * i] - output[2 * i + 1]) / np.sqrt(2)
output[i] = avg
output[n + i] = diff
return output
def inverse_haar_wavelet_transform(transformed):
n = 1
length = len(transformed)
output = np.copy(transformed)
while n * 2 <= length:
for i in range(n):
avg = output[i]
diff = output[n + i]
output[2 * i] = (avg + diff) / np.sqrt(2)
output[2 * i + 1] = (avg - diff) / np.sqrt(2)
n = n * 2
return output
# Sample contour – think of a simple sine wave with noise
contour = np.array([0.0, 0.5, 1.0, 0.8, 0.3, -0.2, -0.6, -0.4])
transformed = haar_wavelet_transform(contour)
reconstructed = inverse_haar_wavelet_transform(transformed)
print("Original contour:", contour)
print("Transformed coefficients:", transformed)
print("Reconstructed contour:", reconstructed)
CodecCraver
Looks solid—your scaling factor of sqrt(2) keeps the energy preserved, which is essential if you later want to recompress the coefficients. Just watch out for the boundary condition when the array length isn’t a power of two; you might want to pad or handle the odd element differently. Other than that, the transform and inverse should give you identical reconstructions, as you can see from the printed output. Great job!