  We develop a general notion of orthogonal wavelets `centered' on an irregular
knot sequence. We present two families of orthogonal wavelets that are
continuous and piecewise polynomial. We develop efficient algorithms to
implement these schemes and apply them to a data set extracted from an ocelot
image. As another application, we construct continuous, piecewise quadratic,
orthogonal wavelet bases on the quasi-crystal lattice consisting of the
$\tau$-integers where $\tau$ is the golden ratio. The resulting spaces then
generate a multiresolution analysis of $L^2(\mathbf{R})$ with scaling factor
$\tau$.
