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java.lang.Objectmfc.vector.Complex2
mfc.geometry.ComplexProjective1
A class that represents points in 1-dimensional complex projective space, also known as the Riemann sphere.
The elements of a Complex2 are interpreted as homogeneous
coordinates.
| Field Summary |
| Fields inherited from class mfc.vector.Complex2 |
aIm, aRe, bIm, bRe, EPS |
| Constructor Summary | |
ComplexProjective1()
Creates the point with homogeneous coordinates (1,0). |
|
ComplexProjective1(Complex a,
Complex b)
Creates the point with homogenous coordinates (a, b). |
|
ComplexProjective1(ComplexProjective1 p)
Creates a copy of p. |
|
ComplexProjective1(double theARe,
double theAIm,
double theBRe,
double theBIm)
Creates the point with homogenous coordinates (a, b),
where a = theARe + i theAIm and b = theBRe + i
theBIm. |
|
| Method Summary | |
void |
apply(Moebius m)
Apply a Moebius transformation. |
boolean |
equals(ComplexProjective1 c)
Indicates whether some other ComplexProjective1 is "equal to" this one. |
boolean |
equals(double aRe1,
double aIm1,
double bRe1,
double bIm1)
|
static boolean |
equals(double aRe1,
double aIm1,
double bRe1,
double bIm1,
double aRe2,
double aIm2)
|
static boolean |
equals(double aRe1,
double aIm1,
double bRe1,
double bIm1,
double aRe2,
double aIm2,
double bRe2,
double bIm2)
|
boolean |
equals(java.lang.Object o)
Indicates whether some other object is "equal to" this one. |
void |
projectTo(Complex z)
Project to the complex plane. |
void |
projectTo(Real3 v)
Project stereographically to the sphere in real 3-space. |
| Methods inherited from class mfc.vector.Complex2 |
assign, assign, assign, assignTimes, assignTimes, assignZero, copy, getA, getA, getB, getB, setA, setB, toString |
| Methods inherited from class java.lang.Object |
clone, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait |
| Constructor Detail |
public ComplexProjective1()
(1,0).
This is the north pole of the Riemann sphere.
public ComplexProjective1(Complex a,
Complex b)
(a, b).
public ComplexProjective1(ComplexProjective1 p)
public ComplexProjective1(double theARe,
double theAIm,
double theBRe,
double theBIm)
(a, b),
where a = theARe + i theAIm and b = theBRe + i
theBIm.
| Method Detail |
public void apply(Moebius m)
public final void projectTo(Complex z)
Project to the complex plane.
The point with coordinates (1,0) is sent to
infinity.
The point with coordinates (0,1) is
sent to zero.
Simply assigns a / b to
z.
z - is set to a/b.public final void projectTo(Real3 v)
Project stereographically to the sphere in real 3-space.
The point with coordinates (1,0) is sent to the
north pole (0,0,1).
The point with coordinates
(0,1) is sent to the south pole (0,0,-1).
The components of v are set to
v.x = 2 Re(a conjugate(b)) / (|a|2 + |b|2)
.
v.y = 2 Im(a conjugate(b)) / (|a|2 + |b|2)
v.z = (|a|2 - |b|2) /
(|a|2 + |b|2)
v - a Real3 used to hand over the result. Must not be
null.
public static final boolean equals(double aRe1,
double aIm1,
double bRe1,
double bIm1,
double aRe2,
double aIm2,
double bRe2,
double bIm2)
public static final boolean equals(double aRe1,
double aIm1,
double bRe1,
double bIm1,
double aRe2,
double aIm2)
public final boolean equals(double aRe1,
double aIm1,
double bRe1,
double bIm1)
public final boolean equals(java.lang.Object o)
public final boolean equals(ComplexProjective1 c)
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