inAball.m

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inAball.m#

Given a collection of balls \(\Omega_\xi\) for centres \(\xi\in\mathcal{P}_{\mathrm{stat}}\), each with radius \(r_\xi\), this algorithm determines if

\[ h_\eta(p) \in \cup_{\xi\in\mathcal{P}_{\mathrm{stat}}}\Omega_\xi, \]

for some \(p\).

This algorithm is used when approximating the steepest descent path \(h_\eta(p)\) for increasing values of \(p\); we want to terminate the path approximation process if \(h_\eta(p)\in \Omega_\xi\) for some \(\xi\in\mathcal{P}_{\mathrm{stat}}\).

[isInBall, outputIndex] = inAball(h, ballCentres, ballRadii)

Inputs#

  • h: The point being tested, typically the farthest point of the contour being traced.

  • ballCentres: Array of centres of balls \(\xi\in\mathcal{P}_{\mathrm{stat}}\).

  • ballRadii: Array of radii of balls \(r_\xi\) for \(\xi\in\mathcal{P}_{\mathrm{stat}}\).

Outputs#

  • isInBall: Boolean value, true if h\(=h_\eta(p)\) is inside of any ball.

  • outputIndex: If isInBall, then this is the index of \(\xi\) in ballCentres. Otherwise, this value is zero.

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