# visualizations of phase

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## 8 matching pages

##### 1: 36.3 Visualizations of Canonical Integrals

##### 2: Philip J. Davis

##### 3: 4.15 Graphics

##### 4: Errata

The scaling error reported on 2016-09-12 by Dan Piponi also applied to contour and density plots for the phase of the hyperbolic umbilic canonical integrals. Scales were corrected in all figures. The interval $-8.4\le \frac{x-y}{\sqrt{2}}\le 8.4$ was replaced by $-12.0\le \frac{x-y}{\sqrt{2}}\le 12.0$ and $-12.7\le \frac{x+y}{\sqrt{2}}\le 4.2$ replaced by $-18.0\le \frac{x+y}{\sqrt{2}}\le 6.0$. All plots and interactive visualizations were regenerated to improve image quality.

(a) Contour plot. | (b) Density plot. |

Figure 36.3.18: Phase of hyperbolic umbilic canonical integral $\mathrm{ph}{\mathrm{\Psi}}^{(\mathrm{H})}\left(x,y,0\right)$.

(a) Contour plot. | (b) Density plot. |

Figure 36.3.19: Phase of hyperbolic umbilic canonical integral $\mathrm{ph}{\mathrm{\Psi}}^{(\mathrm{H})}\left(x,y,1\right)$.

(a) Contour plot. | (b) Density plot. |

Figure 36.3.20: Phase of hyperbolic umbilic canonical integral $\mathrm{ph}{\mathrm{\Psi}}^{(\mathrm{H})}\left(x,y,2\right)$.

(a) Contour plot. | (b) Density plot. |

Figure 36.3.21: Phase of hyperbolic umbilic canonical integral $\mathrm{ph}{\mathrm{\Psi}}^{(\mathrm{H})}\left(x,y,3\right)$.

*Reported 2016-09-28.*

##### 5: About Color Map

###### Phase Mappings

►By painting the surfaces with a color that encodes the phase, $\mathrm{ph}f$, both the magnitude and phase of complex valued functions can be displayed. We offer two options for encoding the phase. ►###### Four Color Phase Mapping

… ►###### Continuous Phase Mapping

…##### 6: 9.9 Zeros

##### 7: 28.33 Physical Applications

Torres-Vega et al. (1998) for Mathieu functions in phase space.

##### 8: DLMF Project News

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