Beispiel #1
0
func (p Place) BackAzimuth(point Place) float64 {

	if (p.Latitude == point.Latitude) && (p.Longitude == point.Longitude) {
		return 0.0
	}

	esq := (1.0 - 1.0/298.25) * (1.0 - 1.0/298.25)
	alat3 := math.Atan(math.Tan(p.Latitude/RadiansToDegrees)*esq) * RadiansToDegrees
	alat4 := math.Atan(math.Tan(point.Latitude/RadiansToDegrees)*esq) * RadiansToDegrees

	rlat1 := alat3 / RadiansToDegrees
	rlat2 := alat4 / RadiansToDegrees
	rdlon := (point.Longitude - p.Longitude) / RadiansToDegrees

	clat1 := math.Cos(rlat1)
	clat2 := math.Cos(rlat2)
	slat1 := math.Sin(rlat1)
	slat2 := math.Sin(rlat2)
	cdlon := math.Cos(rdlon)
	sdlon := math.Sin(rdlon)

	ybaz := -sdlon * clat1
	xbaz := clat2*slat1 - slat2*clat1*cdlon

	baz := RadiansToDegrees * math.Atan2(ybaz, xbaz)

	if baz < 0.0 {
		baz += 360.0
	}

	return baz
}
Beispiel #2
0
func (view *ViewData) Initialize() {
	twoPi := 8.0 * math.Atan(1.0)
	halfCone := float64(view.FieldOfView) * float64(twoPi/360.0) / 2.0
	adjustedHalfCone := math.Asin(float64(view.ScreenWidth) * math.Sin(halfCone) / float64(view.StandardScreenWidth))
	var worldToScreen float64

	view.HalfScreenWidth = view.ScreenWidth / 2
	view.HalfScreenHeight = view.ScreenHeight / 2

	// if there's a round-off error in half_cone, we want to make the cone too big (so when we clip lines to the edge of the screen they're actually off the screen, thus +1.0)
	view.HalfCone = Angle(adjustedHalfCone*(float64(NumberOfAngles))/twoPi + 1.0)

	// calculate world_to_screen; we could calculate this with standard_screen_width/2 and the old half_cone and get the same result
	worldToScreen = float64(view.HalfScreenWidth) / math.Tan(adjustedHalfCone)
	tmp0 := int16((worldToScreen / float64(view.HorizontalScale)) + 0.5)
	tmp1 := int16((worldToScreen / float64(view.VerticalScale)) + 0.5)
	view.WorldToScreen.X = tmp0
	view.RealWorldToScreen.X = tmp0
	view.WorldToScreen.Y = tmp1
	view.RealWorldToScreen.Y = tmp1

	// cacluate the vertical cone angle; again, overflow instead of underflow when rounding
	view.HalfVerticalCone = Angle(NumberOfAngles*math.Atan((float64(view.HalfScreenHeight*view.VerticalScale)/worldToScreen))/twoPi + 1.0)

	// calculate left edge vector
	view.UntransformedLeftEdge.I = WorldDistance(view.WorldToScreen.X)
	view.UntransformedLeftEdge.J = WorldDistance(-view.HalfScreenWidth)

	// calculate right edge vector (negative, so it clips in the right direction)
	view.UntransformedRightEdge.I = WorldDistance(-view.WorldToScreen.X)
	view.UntransformedRightEdge.J = WorldDistance(-view.HalfScreenWidth)

	// reset any effects
	view.Effect = cseries.None
}
Beispiel #3
0
func (p Place) Distance(point Place) float64 {

	if (p.Latitude == point.Latitude) && (p.Longitude == point.Longitude) {
		return 0.0
	}

	esq := (1.0 - 1.0/298.25) * (1.0 - 1.0/298.25)
	alat3 := math.Atan(math.Tan(p.Latitude/RadiansToDegrees)*esq) * RadiansToDegrees
	alat4 := math.Atan(math.Tan(point.Latitude/RadiansToDegrees)*esq) * RadiansToDegrees

	rlat1 := alat3 / RadiansToDegrees
	rlat2 := alat4 / RadiansToDegrees
	rdlon := (point.Longitude - p.Longitude) / RadiansToDegrees

	clat1 := math.Cos(rlat1)
	clat2 := math.Cos(rlat2)
	slat1 := math.Sin(rlat1)
	slat2 := math.Sin(rlat2)
	cdlon := math.Cos(rdlon)

	cdel := slat1*slat2 + clat1*clat2*cdlon
	switch {
	case cdel > 1.0:
		cdel = 1.0
	case cdel < -1.0:
		cdel = -1.0
	}

	return RadiansToKm * math.Acos(cdel)
}
Beispiel #4
0
func (p Place) Azimuth(point Place) float64 {

	if (p.Latitude == point.Latitude) && (p.Longitude == point.Longitude) {
		return 0.0
	}

	esq := (1.0 - 1.0/298.25) * (1.0 - 1.0/298.25)
	alat3 := math.Atan(math.Tan(p.Latitude/RadiansToDegrees)*esq) * RadiansToDegrees
	alat4 := math.Atan(math.Tan(point.Latitude/RadiansToDegrees)*esq) * RadiansToDegrees

	rlat1 := alat3 / RadiansToDegrees
	rlat2 := alat4 / RadiansToDegrees
	rdlon := (point.Longitude - p.Longitude) / RadiansToDegrees

	clat1 := math.Cos(rlat1)
	clat2 := math.Cos(rlat2)
	slat1 := math.Sin(rlat1)
	slat2 := math.Sin(rlat2)
	cdlon := math.Cos(rdlon)
	sdlon := math.Sin(rdlon)

	yazi := sdlon * clat2
	xazi := clat1*slat2 - slat1*clat2*cdlon

	azi := RadiansToDegrees * math.Atan2(yazi, xazi)

	if azi < 0.0 {
		azi += 360.0
	}

	return azi
}
Beispiel #5
0
// AnomalyDistance returns true anomaly and distance for near-parabolic orbits.
//
// Distance r returned in AU.
// An error is returned if the algorithm fails to converge.
func (e *Elements) AnomalyDistance(jde float64) (ν unit.Angle, r float64, err error) {
	// fairly literal translation of code on p. 246
	q1 := base.K * math.Sqrt((1+e.Ecc)/e.PDis) / (2 * e.PDis) // line 20
	g := (1 - e.Ecc) / (1 + e.Ecc)                            // line 20

	t := jde - e.TimeP // line 22
	if t == 0 {        // line 24
		return 0, e.PDis, nil
	}
	d1, d := 10000., 1e-9        // line 14
	q2 := q1 * t                 // line 28
	s := 2. / (3 * math.Abs(q2)) // line 30
	s = 2 / math.Tan(2*math.Atan(math.Cbrt(math.Tan(math.Atan(s)/2))))
	if t < 0 { // line 34
		s = -s
	}
	if e.Ecc != 1 { // line 36
		l := 0 // line 38
		for {
			s0 := s // line 40
			z := 1.
			y := s * s
			g1 := -y * s
			q3 := q2 + 2*g*s*y/3 // line 42
			for {
				z += 1                          // line 44
				g1 = -g1 * g * y                // line 46
				z1 := (z - (z+1)*g) / (2*z + 1) // line 48
				f := z1 * g1                    // line 50
				q3 += f                         // line 52
				if z > 50 || math.Abs(f) > d1 { // line 54
					return 0, 0, errors.New("No convergence")
				}
				if math.Abs(f) <= d { // line 56
					break
				}
			}
			l++ // line 58
			if l > 50 {
				return 0, 0, errors.New("No convergence")
			}
			for {
				s1 := s // line 60
				s = (2*s*s*s/3 + q3) / (s*s + 1)
				if math.Abs(s-s1) <= d { // line 62
					break
				}
			}
			if math.Abs(s-s0) <= d { // line 64
				break
			}
		}
	}
	ν = unit.Angle(2 * math.Atan(s))               // line 66
	r = e.PDis * (1 + e.Ecc) / (1 + e.Ecc*ν.Cos()) // line 68
	if ν < 0 {                                     // line 70
		ν += 2 * math.Pi
	}
	return
}
func (pt *Point) cartesianToGeographic(meridien float64, a float64, e float64, eps float64) {

	x := pt.X
	y := pt.Y
	z := pt.Z

	lon := meridien + math.Atan(y/x)

	module := math.Sqrt(x*x + y*y)

	phi_0 := math.Atan(z / (module * (1 - (a*e*e)/math.Sqrt(x*x+y*y+z*z))))

	phi_i := math.Atan(z / module / (1 - a*e*e*math.Cos(phi_0)/(module*math.Sqrt(1-e*e*math.Sin(phi_0)*math.Sin(phi_0)))))

	delta := 100.0
	for delta > eps {

		phi_0 = phi_i
		phi_i = math.Atan(z / module / (1 - a*e*e*math.Cos(phi_0)/(module*math.Sqrt(1-e*e*math.Sin(phi_0)*math.Sin(phi_0)))))
		delta = math.Abs(phi_i - phi_0)
	}
	he := module/math.Cos(phi_i) - a/math.Sqrt(1-e*e*math.Sin(phi_i)*math.Sin(phi_i))

	pt.X = lon
	pt.Y = phi_i
	pt.Z = he
	pt.Unit = Radian
}
Beispiel #7
0
func (sfc *pdfSurface) Skew(xRadians float64, yRadians float64) {

	x := math.Atan(xRadians)
	y := math.Atan(yRadians)

	sfc.alterMatrix(1, x, y, 1, 0, 0)
}
Beispiel #8
0
func (self *Calc) CalculateFunction(funcName string, arg32 float32) float32 {
	if len(self.errors) > 0 {
		return 1
	}

	var result float64
	arg := float64(arg32)
	switch funcName {
	case "sin":
		result = math.Sin(self.DegToRad(arg))
	case "cos":
		result = math.Cos(self.DegToRad(arg))
	case "tg":
		result = math.Tan(self.DegToRad(arg))
	case "ctg":
		result = 1.0 / math.Tan(self.DegToRad(arg))
	case "arcsin":
		result = self.RadToDeg(math.Asin(arg))
	case "arccos":
		result = self.RadToDeg(math.Acos(arg))
	case "arctg":
		result = self.RadToDeg(math.Atan(arg))
	case "arcctg":
		result = self.RadToDeg(math.Atan(1 / arg))
	case "sqrt":
		result = math.Sqrt(arg)
	default:
		self.errors = append(self.errors, "Unknown identifier "+funcName)
		return 1
	}

	return float32(result)
}
Beispiel #9
0
// ProbContestSmall computes the probability for a contest between u and v where u wins if it's
// the smaller value. φ ∃ [0,1] is a scaling factor that helps v win even if it's not smaller.
// If φ==0, deterministic analysis is carried out. If φ==1, probabilistic analysis is carried out.
// As φ → 1, v "gets more help".
func ProbContestSmall(u, v, φ float64) float64 {
	u = math.Atan(u)/math.Pi + 1.5
	v = math.Atan(v)/math.Pi + 1.5
	if u < v {
		return v / (v + φ*u)
	}
	if u > v {
		return φ * v / (φ*v + u)
	}
	return 0.5
}
Beispiel #10
0
// Get matrix rotation as Euler angles in degrees
func (m *Mat3) GetEuler() *V3 {
	x := math.Atan((-m.matrix[5]) / m.matrix[8])
	y := math.Asin(m.matrix[2])
	z := math.Atan((-m.matrix[1]) / m.matrix[0])

	// Convert to Degrees
	x *= 180 / math.Pi
	y *= 180 / math.Pi
	z *= 180 / math.Pi

	return NewV3(x, y, z)
}
Beispiel #11
0
// Get M rotation as Euler angles in degrees
func (m *Mat3) GetEuler() *Vec3 {
	x := math.Atan((-m.M[5]) / m.M[8])
	y := math.Asin(m.M[2])
	z := math.Atan((-m.M[1]) / m.M[0])

	// Convert to Degrees
	x *= 180 / math.Pi
	y *= 180 / math.Pi
	z *= 180 / math.Pi

	return V3(x, y, z)
}
Beispiel #12
0
func latitudeFromLatitudeISO(lat_iso float64, e float64, eps float64) float64 {

	phi_0 := 2*math.Atan(math.Exp(lat_iso)) - math.Pi/2
	phi_i := 2*math.Atan(math.Pow((1+e*math.Sin(phi_0))/(1-e*math.Sin(phi_0)), e/2)*math.Exp(lat_iso)) - math.Pi/2

	delta := 100.0
	for delta > eps {
		phi_0 = phi_i
		phi_i = 2*math.Atan(math.Pow((1+e*math.Sin(phi_0))/(1-e*math.Sin(phi_0)), e/2.0)*math.Exp(lat_iso)) - math.Pi/2
		delta = math.Abs(phi_i - phi_0)
	}
	return phi_i
}
func main() {
	fmt.Printf("sin(%9.6f deg) = %f\n", d, math.Sin(d*math.Pi/180))
	fmt.Printf("sin(%9.6f rad) = %f\n", r, math.Sin(r))
	fmt.Printf("cos(%9.6f deg) = %f\n", d, math.Cos(d*math.Pi/180))
	fmt.Printf("cos(%9.6f rad) = %f\n", r, math.Cos(r))
	fmt.Printf("tan(%9.6f deg) = %f\n", d, math.Tan(d*math.Pi/180))
	fmt.Printf("tan(%9.6f rad) = %f\n", r, math.Tan(r))
	fmt.Printf("asin(%f) = %9.6f deg\n", s, math.Asin(s)*180/math.Pi)
	fmt.Printf("asin(%f) = %9.6f rad\n", s, math.Asin(s))
	fmt.Printf("acos(%f) = %9.6f deg\n", c, math.Acos(c)*180/math.Pi)
	fmt.Printf("acos(%f) = %9.6f rad\n", c, math.Acos(c))
	fmt.Printf("atan(%f) = %9.6f deg\n", t, math.Atan(t)*180/math.Pi)
	fmt.Printf("atan(%f) = %9.6f rad\n", t, math.Atan(t))
}
Beispiel #14
0
/**
* Returns the yaw pitch and roll angles, respectively defined as the angles in radians between
* the Earth North and the IMU Z axis (yaw), the Earth ground plane and the IMU Y axis (pitch)
* and the Earth ground plane and the IMU X axis (roll).
*
* Returns Yaw, Pitch and Roll angles in radians
**/
func (imu *ImuMayhony) Update(when int64, gx, gy, gz, ax, ay, az, mx, my, mz float32) (yaw, pitch, roll float32) {
	var (
		gravx, gravy, gravz float64 // estimated gravity direction
	)
	imu.sampleFreq = 1.0 / (float32(when-imu.lastUpdate) / 1000000000.0) // nanoseconds to fractions of a second
	imu.lastUpdate = when
	ahrsUpdate(imu, gx, gy, gz, ax, ay, az, mx, my, mz)
	gravx = float64(2.0 * (imu.q1*imu.q3 - imu.q0*imu.q2))
	gravy = float64(2.0 * (imu.q0*imu.q1 + imu.q2*imu.q3))
	gravz = float64(imu.q0*imu.q0 - imu.q1*imu.q1 - imu.q2*imu.q2 + imu.q3*imu.q3)
	yaw = float32(math.Atan2(float64(2.0*imu.q1*imu.q2-2.0*imu.q0*imu.q3), float64(2.0*imu.q0*imu.q0+2.0*imu.q1*imu.q1-1.0)))
	pitch = float32(math.Atan(gravx / math.Sqrt(gravy*gravy+gravz*gravz)))
	roll = float32(math.Atan(gravy / math.Sqrt(gravx*gravx+gravz*gravz)))
	return
}
//GridToGeodetic converts RT90 coordinates to WGS84
func GridToGeodetic(x, y float64) (float64, float64) {

	if CentralMeridian == 31337.0 {
		return 0.0, 0.0
	}

	e2 := Flattening * (2.0 - Flattening)
	n := Flattening / (2.0 - Flattening)
	a_roof := Axis / (1.0 + n) * (1.0 + n*n/4.0 + n*n*n*n/64.0)
	delta1 := n/2.0 - 2.0*n*n/3.0 + 37.0*n*n*n/96.0 - n*n*n*n/360.0
	delta2 := n*n/48.0 + n*n*n/15.0 - 437.0*n*n*n*n/1440.0
	delta3 := 17.0*n*n*n/480.0 - 37*n*n*n*n/840.0
	delta4 := 4397.0 * n * n * n * n / 161280.0

	Astar := e2 + e2*e2 + e2*e2*e2 + e2*e2*e2*e2
	Bstar := -(7.0*e2*e2 + 17.0*e2*e2*e2 + 30.0*e2*e2*e2*e2) / 6.0
	Cstar := (224.0*e2*e2*e2 + 889.0*e2*e2*e2*e2) / 120.0
	Dstar := -(4279.0 * e2 * e2 * e2 * e2) / 1260.0

	DegToRad := math.Pi / 180
	LambdaZero := CentralMeridian * DegToRad
	xi := (x - FalseNorthing) / (Scale * a_roof)
	eta := (y - FalseEasting) / (Scale * a_roof)
	xi_prim := xi - delta1*math.Sin(2.0*xi)*math.Cosh(2.0*eta) - delta2*math.Sin(4.0*xi)*math.Cosh(4.0*eta) - delta3*math.Sin(6.0*xi)*math.Cosh(6.0*eta) - delta4*math.Sin(8.0*xi)*math.Cosh(8.0*eta)
	eta_prim := eta - delta1*math.Cos(2.0*xi)*math.Sinh(2.0*eta) - delta2*math.Cos(4.0*xi)*math.Sinh(4.0*eta) - delta3*math.Cos(6.0*xi)*math.Sinh(6.0*eta) - delta4*math.Cos(8.0*xi)*math.Sinh(8.0*eta)
	phi_star := math.Asin(math.Sin(xi_prim) / math.Cosh(eta_prim))
	delta_lambda := math.Atan(math.Sinh(eta_prim) / math.Cos(xi_prim))
	lon_radian := LambdaZero + delta_lambda
	lat_radian := phi_star + math.Sin(phi_star)*math.Cos(phi_star)*(Astar+Bstar*math.Pow(math.Sin(phi_star), 2)+Cstar*math.Pow(math.Sin(phi_star), 4)+Dstar*math.Pow(math.Sin(phi_star), 6))

	return lat_radian * 180.0 / math.Pi, lon_radian * 180.0 / math.Pi
}
func fromPixelToLL(px [2]float64, zoom uint64) [2]float64 {
	e := gp.zc[zoom]
	f := (px[0] - e[0]) / gp.Bc[zoom]
	g := (px[1] - e[1]) / -gp.Cc[zoom]
	h := 180.0 / math.Pi * (2*math.Atan(math.Exp(g)) - 0.5*math.Pi)
	return [2]float64{f, h}
}
Beispiel #17
0
// PointArea returns the area on the unit sphere for the triangle defined by the
// given points.
//
// This method is based on l'Huilier's theorem,
//
//   tan(E/4) = sqrt(tan(s/2) tan((s-a)/2) tan((s-b)/2) tan((s-c)/2))
//
// where E is the spherical excess of the triangle (i.e. its area),
//       a, b, c are the side lengths, and
//       s is the semiperimeter (a + b + c) / 2.
//
// The only significant source of error using l'Huilier's method is the
// cancellation error of the terms (s-a), (s-b), (s-c). This leads to a
// *relative* error of about 1e-16 * s / min(s-a, s-b, s-c). This compares
// to a relative error of about 1e-15 / E using Girard's formula, where E is
// the true area of the triangle. Girard's formula can be even worse than
// this for very small triangles, e.g. a triangle with a true area of 1e-30
// might evaluate to 1e-5.
//
// So, we prefer l'Huilier's formula unless dmin < s * (0.1 * E), where
// dmin = min(s-a, s-b, s-c). This basically includes all triangles
// except for extremely long and skinny ones.
//
// Since we don't know E, we would like a conservative upper bound on
// the triangle area in terms of s and dmin. It's possible to show that
// E <= k1 * s * sqrt(s * dmin), where k1 = 2*sqrt(3)/Pi (about 1).
// Using this, it's easy to show that we should always use l'Huilier's
// method if dmin >= k2 * s^5, where k2 is about 1e-2. Furthermore,
// if dmin < k2 * s^5, the triangle area is at most k3 * s^4, where
// k3 is about 0.1. Since the best case error using Girard's formula
// is about 1e-15, this means that we shouldn't even consider it unless
// s >= 3e-4 or so.
func PointArea(a, b, c Point) float64 {
	sa := float64(b.Angle(c.Vector))
	sb := float64(c.Angle(a.Vector))
	sc := float64(a.Angle(b.Vector))
	s := 0.5 * (sa + sb + sc)
	if s >= 3e-4 {
		// Consider whether Girard's formula might be more accurate.
		dmin := s - math.Max(sa, math.Max(sb, sc))
		if dmin < 1e-2*s*s*s*s*s {
			// This triangle is skinny enough to use Girard's formula.
			ab := a.PointCross(b)
			bc := b.PointCross(c)
			ac := a.PointCross(c)
			area := math.Max(0.0, float64(ab.Angle(ac.Vector)-ab.Angle(bc.Vector)+bc.Angle(ac.Vector)))

			if dmin < s*0.1*area {
				return area
			}
		}
	}

	// Use l'Huilier's formula.
	return 4 * math.Atan(math.Sqrt(math.Max(0.0, math.Tan(0.5*s)*math.Tan(0.5*(s-sa))*
		math.Tan(0.5*(s-sb))*math.Tan(0.5*(s-sc)))))
}
Beispiel #18
0
func TestCapContainsCell(t *testing.T) {
	faceRadius := math.Atan(math.Sqrt2)
	for face := 0; face < 6; face++ {
		// The cell consisting of the entire face.
		rootCell := CellFromCellID(CellIDFromFace(face))

		// A leaf cell at the midpoint of the v=1 edge.
		edgeCell := CellFromPoint(Point{faceUVToXYZ(face, 0, 1-eps)})

		// A leaf cell at the u=1, v=1 corner
		cornerCell := CellFromPoint(Point{faceUVToXYZ(face, 1-eps, 1-eps)})

		// Quick check for full and empty caps.
		if !full.ContainsCell(rootCell) {
			t.Errorf("Cap(%v).ContainsCell(%v) = %t; want = %t", full, rootCell, false, true)
		}

		// Check intersections with the bounding caps of the leaf cells that are adjacent to
		// cornerCell along the Hilbert curve.  Because this corner is at (u=1,v=1), the curve
		// stays locally within the same cube face.
		first := cornerCell.id.Advance(-3)
		last := cornerCell.id.Advance(4)
		for id := first; id < last; id = id.Next() {
			c := CellFromCellID(id).CapBound()
			if got, want := c.ContainsCell(cornerCell), id == cornerCell.id; got != want {
				t.Errorf("Cap(%v).ContainsCell(%v) = %t; want = %t", c, cornerCell, got, want)
			}
		}

		for capFace := 0; capFace < 6; capFace++ {
			// A cap that barely contains all of capFace.
			center := unitNorm(capFace)
			covering := CapFromCenterAngle(center, s1.Angle(faceRadius+eps))
			if got, want := covering.ContainsCell(rootCell), capFace == face; got != want {
				t.Errorf("Cap(%v).ContainsCell(%v) = %t; want = %t", covering, rootCell, got, want)
			}
			if got, want := covering.ContainsCell(edgeCell), center.Vector.Dot(edgeCell.id.Point().Vector) > 0.1; got != want {
				t.Errorf("Cap(%v).ContainsCell(%v) = %t; want = %t", covering, edgeCell, got, want)
			}
			if got, want := covering.ContainsCell(edgeCell), covering.IntersectsCell(edgeCell); got != want {
				t.Errorf("Cap(%v).ContainsCell(%v) = %t; want = %t", covering, edgeCell, got, want)
			}
			if got, want := covering.ContainsCell(cornerCell), capFace == face; got != want {
				t.Errorf("Cap(%v).ContainsCell(%v) = %t; want = %t", covering, cornerCell, got, want)
			}

			// A cap that barely intersects the edges of capFace.
			bulging := CapFromCenterAngle(center, s1.Angle(math.Pi/4+eps))
			if bulging.ContainsCell(rootCell) {
				t.Errorf("Cap(%v).ContainsCell(%v) = %t; want = %t", bulging, rootCell, true, false)
			}
			if got, want := bulging.ContainsCell(edgeCell), capFace == face; got != want {
				t.Errorf("Cap(%v).ContainsCell(%v) = %t; want = %t", bulging, edgeCell, got, want)
			}
			if bulging.ContainsCell(cornerCell) {
				t.Errorf("Cap(%v).ContainsCell(%v) = %t; want = %t", bulging, cornerCell, true, false)
			}
		}
	}
}
Beispiel #19
0
// Generates sample from general Levy-stable distibution.
func Sample(alpha float64, beta float64, mu float64, sigma float64) float64 {
	if beta == 0.0 {
		return symmetric(alpha, mu, sigma)
	}

	v := math.Pi * (rand.Float64() - 0.5)

	w := 0.0
	for w == 0.0 {
		w = rand.ExpFloat64()
	}

	if alpha == 1.0 {
		x := ((0.5*math.Pi+beta*v)*math.Tan(v) -
			beta*math.Log(0.5*math.Pi*w*math.Cos(v)/(0.5*math.Pi+beta*v))) / (0.5 * math.Pi)
		return sigma*x + beta*sigma*math.Log(sigma)/(0.5*math.Pi) + mu
	}

	t := beta * math.Tan(0.5*math.Pi*alpha)
	s := math.Pow(1.0+t*t, 1.0/(2.0*alpha))
	b := math.Atan(t) / alpha
	x := s * math.Sin(alpha*(v+b)) *
		math.Pow(math.Cos(v-alpha*(v+b))/w, (1.0-alpha)/alpha) /
		math.Pow(math.Cos(v), 1.0/alpha)
	return sigma*x + mu
}
Beispiel #20
0
func TestTofloat(t *testing.T) {
	oldval := cfg.UseRadians
	cfg.UseRadians = true
	type test struct {
		in  string
		out float64
	}
	var tests []test = []test{
		{"2.5+2.5", 2.5 + 2.5},
		{"2.5*2.5", 2.5 * 2.5},
		{"3/2", 3. / 2.},
		{"2^10", math.Pow(2, 10)},
		{"sqrt(2)", math.Sqrt(2)},
		{"sin(2)", math.Sin(2)},
		{"cos(2)", math.Cos(2)},
		{"tan(2)", math.Tan(2)},
		{"arcsin(0.3)", math.Asin(0.3)},
		{"arccos(0.3)", math.Acos(0.3)},
		{"arctan(0.3)", math.Atan(0.3)},
		{"ln(2)", math.Log(2)},
		{"log(2)", math.Log10(2)},
	}
	for _, k := range tests {
		result := TextToCas(k.in).Tofloat()
		if result != k.out {
			t.Errorf("Tofloat: In:%v Out:%v Result:%v",
				k.in, k.out, result)
		}
	}
	cfg.UseRadians = oldval
}
Beispiel #21
0
func (p *PerspectiveCamera) UpdateProjectionMatrix() {

	var fov = math3d.RadToDeg(2 * math.Atan(math.Tan(math3d.DegToRad(p.Fov)*0.5)/p.Zoom))

	if p.FullWidth > 0 {

		var aspect = p.FullWidth / p.FullHeight
		var top = math.Tan(math3d.DegToRad(fov*0.5)) * p.Near
		var bottom = -top
		var left = aspect * bottom
		var right = aspect * top
		var width = math.Abs(right - left)
		var height = math.Abs(top - bottom)

		p.ProjectionMatrix.MakeFrustum(
			left+p.X*width/p.FullWidth,
			left+(p.X+p.Width)*width/p.FullWidth,
			top-(p.Y+p.Height)*height/p.FullHeight,
			top-p.Y*height/p.FullHeight,
			p.Near,
			p.Far,
		)
	} else {
		p.ProjectionMatrix.MakePerspective(fov, p.Aspect, p.Near, p.Far)
	}
}
Beispiel #22
0
// ParallaxConstants computes parallax constants ρ sin φ′ and ρ cos φ′.
//
// Arguments are geographic latitude φ in radians and height h
// in meters above the ellipsoid.
func (e Ellipsoid) ParallaxConstants(φ, h float64) (s, c float64) {
	boa := 1 - e.Fl
	su, cu := math.Sincos(math.Atan(boa * math.Tan(φ)))
	s, c = math.Sincos(φ)
	hoa := h * 1e-3 / e.Er
	return su*boa + hoa*s, cu + hoa*c
}
Beispiel #23
0
// ParallaxConstants computes parallax constants ρ sin φ′ and ρ cos φ′.
//
// Arguments are geographic latitude φ and height h above the ellipsoid.
// For e.Er in Km, h must be in meters.
func (e Ellipsoid) ParallaxConstants(φ unit.Angle, h float64) (s, c float64) {
	boa := 1 - e.Fl
	su, cu := math.Sincos(math.Atan(boa * φ.Tan()))
	s, c = φ.Sincos()
	hoa := h * 1e-3 / e.Er
	return su*boa + hoa*s, cu + hoa*c
}
Beispiel #24
0
func (pdf *PdfBergstrom) ScaledValue(x, alpha, beta float64) (float64, error) {

	var err error
	zeta := beta * math.Tan(0.5*math.Pi*alpha)
	eps := pdf.eps / x * math.Pi
	done := false
	n := 1
	sum := 0.0
	for !done {
		a := 1.0
		if n%2 == 0 {
			a = -1.0
		}
		a *= math.Gamma(float64(n)*alpha+1) / math.Gamma(float64(n)+1)
		a *= math.Pow(1+zeta*zeta, 0.5*float64(n))
		a *= math.Sin(float64(n) * (0.5*math.Pi*alpha + math.Atan(zeta)))

		delta := a * math.Pow(x, -alpha*float64(n))
		sum += delta

		if math.Abs(delta) < eps {
			done = true
		}
		if n >= pdf.limit {
			done = true
			err = fmt.Errorf("Iteration limit in tail approximation exceeded (%d)", pdf.limit)
		}
		n++
	}
	sum /= x * math.Pi
	return sum, err
}
Beispiel #25
0
func (v *Vec3) ToSpherical() (c *SphVec3) {
	// from Wikipedia article
	c.r = v.Length()
	c.phi = math.Atan2(v.y, v.x)
	c.theta = math.Atan(v.z / c.r)
	return
}
Beispiel #26
0
// Write text on line from p1 to p2, with cntGrids values as given in vals.
// Prerequisites: vals[] is linear
func (s *SVG) Label(x1, y1, x2, y2 int, vals []float64, cntGrids int, a Att) {
	g := s.GID("label", a)
	g.AddAtt(false, Att{"fill": "black"})
	xDiff := float64(x2 - x1)
	yDiff := float64(y2 - y1)
	angle := math.Abs(math.Atan(yDiff / xDiff))

	// Find increments
	max := max(vals...)
	min := min(vals...)
	valIncr := (max - min) / float64(cntGrids)
	xIncr := float64(xDiff) / float64(cntGrids) * math.Cos(angle)
	yIncr := float64(yDiff) / float64(cntGrids) * math.Sin(angle)

	// Start values
	val := min
	x := float64(x1)
	y := float64(y1)

	// Draw text
	for i := 0; i <= cntGrids; i++ {
		g.Text(round(x), round(y), fmt.Sprintf("%.2f", val), nil)
		val += valIncr
		x += xIncr
		y += yIncr
	}
}
Beispiel #27
0
func xatan() {
	r := popr()
	if r< -math.Pi/2+paminstr.Eps || r>math.Pi/2-paminstr.Eps {
		panic("atan argument out of [-Pi/2, Pi/2]")
	}
	pushr(math.Atan(r))
}
Beispiel #28
0
// Generate a warped frequency curve for warping coefficient _alpha_
// and return a normalized vector of length _vectorlength_ containing
// equally spaced points between 0 and PI
func WarpingVector(alpha float64, vectorlength int) []float64 {
	var i int
	var step float64
	var warpingvector []float64

	step = math.Pi / float64(vectorlength)

	warpingvector = make([]float64, vectorlength, vectorlength)

	for i = 0; i < vectorlength; i++ {
		var warpfreq, omega float64
		var num, den float64
		omega = step * float64(i)
		num = (1 - alpha*alpha) * math.Sin(omega)
		den = (1+alpha*alpha)*math.Cos(omega) - 2*alpha
		warpfreq = math.Atan(num / den)

		// Wrap the phase if it becomes negative
		if warpfreq < 0 {
			warpfreq += math.Pi
		}

		warpingvector[i] = warpfreq
	}

	// Normalize the Vector. Values are positive and monotonically
	// increasing, so divide by max
	max := warpingvector[vectorlength-1]
	for i = 0; i < vectorlength; i++ {
		warpingvector[i] /= max
	}
	return warpingvector
}
Beispiel #29
0
func convertLABToHue(a, b float64) float64 {
	var bias float64 = 0
	if a >= 0 && b == 0 {
		return 0
	}
	if a < 0 && b == 0 {
		return 180
	}
	if a == 0 && b > 0 {
		return 90
	}
	if a == 0 && b < 0 {
		return 270
	}
	if a > 0 && b > 0 {
		bias = 0
	}
	if a < 0 {
		bias = 180
	}
	if a > 0 && b < 0 {
		bias = 360
	}
	return (convertRadToDeg(math.Atan(b/a)) + bias)
}
Beispiel #30
0
func asrTime(loc Location, julT, dhuhr, factor float64) float64 {
	_, dec := sunPosition(julT)
	angle := -math.Atan(1 / (factor + math.Tan(rad(math.Abs(loc.Lat-dec)))))
	aTime := timeAngle(loc.Lat, julT, dhuhr, angle, 1)
	//fmt.Println(angle, aTime)
	return aTime
}