feat: 扩展天文计算能力
- 新增日食、月食、本地可见性、中心线、半影区域、SVG 图示与沙罗周期信息 - 新增行星冲合、留、方照、物理星历、视直径、相位、亮肢角、轨道节点等计算 - 新增木星伽利略卫星位置、现象与接触事件计算 - 新增恒星星表、星座判定、自行修正与观测辅助能力 - 新增 coord、formula、orbit、sundial、lite/sun、lite/moon 等扩展包 - 完善农历年号、月相英文别名、视差角、大气质量、折射、日晷与双星计算 - 增加 NASA、JPL Horizons、IMCCE 等回归测试数据与基线测试 - 重构基础算法文件组织，补充大量公开 API 注释和语义回归测试 - 更新中文和英文 README，补充示例、精度说明、SVG 配图
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package sundial
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import (
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"math"
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"time"
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"b612.me/astro/sun"
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)
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// PlanarDial 平面日晷参数 / planar-sundial parameters.
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//
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// Latitude 为地理纬度（北正南负）；PlaneNormalAzimuth 为日晷盘面法线的方位角，
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// 按正北为 0°、向东增加；PlaneNormalZenithDistance 为盘面法线的天顶距，0° 表示水平日晷，
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// 90° 表示垂直日晷；StylusLength 为垂直于盘面的直晷针长度。
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//
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// 坐标系沿本章通用约定：x 轴位于盘面内且保持水平，y 轴沿盘面最大坡度向上，
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// x 正向为右侧，y 正向为上坡方向。
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type PlanarDial struct {
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Latitude float64
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PlaneNormalAzimuth float64
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PlaneNormalZenithDistance float64
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StylusLength float64
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}
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// PlanarShadowPoint 平面日晷影尖位置 / shadow-tip position on a planar sundial.
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//
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// X/Y 为影尖在盘面坐标系中的坐标；DenominatorQ 对应书中公式里的 Q；
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// SunAboveHorizon 表示太阳在地平线上方；PlaneIlluminated 表示盘面被太阳照亮；
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// Illuminated 为前两者同时满足。
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type PlanarShadowPoint struct {
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X float64
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Y float64
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DenominatorQ float64
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SunAboveHorizon bool
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PlaneIlluminated bool
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Illuminated bool
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}
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// PlanarGeometry 平面日晷几何量 / derived planar-sundial geometry.
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//
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// CenterX/CenterY 为日晷中心（极轴晷针固定点）坐标；PolarStylusLength 为极轴晷针长度；
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// PolarStylusPlaneAngle 为极轴晷针与盘面的夹角。HasFiniteCenter 为 false 时，
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// 表示极轴晷针与盘面平行，中心退化到无穷远处。
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type PlanarGeometry struct {
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CenterX float64
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CenterY float64
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PolarStylusLength float64
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PolarStylusPlaneAngle float64
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HasFiniteCenter bool
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}
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// HourAngleInterval 时角区间 / hour-angle interval.
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//
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// Start/End 均为有符号太阳时角，单位度，满足 Start <= End。
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// 约定取值范围为 [-180, 180]，用于表达一天中的一段连续时角。
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type HourAngleInterval struct {
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Start float64
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End float64
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}
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// DeclinationCurveSample 赤纬曲线采样点 / sampled point on a declination curve.
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//
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// HourAngle 为采样点的太阳时角；Point 为该时角下的影尖位置与照明状态。
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type DeclinationCurveSample struct {
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HourAngle float64
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Point PlanarShadowPoint
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}
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// DeclinationCurveSegment 赤纬曲线分段 / one illuminated segment of a declination curve.
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//
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// Interval 给出该段对应的连续受光时角范围；Samples 为该段内部的采样点。
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type DeclinationCurveSegment struct {
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Declination float64
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Interval HourAngleInterval
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Samples []DeclinationCurveSample
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}
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// TimeLineSample 时间线采样点 / sampled point on a mean-time or zone-time line.
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//
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// Date 为该采样点对应的绝对时刻；其日期来自输入 date，钟面时间由调用参数指定。
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// Declination 为该采样瞬时的太阳赤纬；HourAngle 为换算后的视太阳时角；
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// Point 为该时角下的影尖位置与照明状态。
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type TimeLineSample struct {
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Date time.Time
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Declination float64
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HourAngle float64
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Point PlanarShadowPoint
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}
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// EquatorialNorthDial 北面赤道日晷 / north-face equatorial dial.
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//
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// 北半球时用于春夏半年（太阳赤纬为正）；南半球也可直接按公式使用。
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func EquatorialNorthDial(latitude, stylusLength float64) PlanarDial {
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return PlanarDial{
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Latitude: latitude,
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PlaneNormalAzimuth: 0,
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PlaneNormalZenithDistance: 90 - latitude,
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StylusLength: stylusLength,
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}
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}
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// EquatorialSouthDial 南面赤道日晷 / south-face equatorial dial.
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//
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// 北半球时用于秋冬半年（太阳赤纬为负）；南半球也可直接按公式使用。
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func EquatorialSouthDial(latitude, stylusLength float64) PlanarDial {
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return PlanarDial{
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Latitude: latitude,
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PlaneNormalAzimuth: 180,
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PlaneNormalZenithDistance: 90 + latitude,
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StylusLength: stylusLength,
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}
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}
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// HorizontalDial 水平日晷 / horizontal dial.
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//
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// 该构造器采用经典水平日晷的坐标约定：x 轴向东，y 轴向北。
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func HorizontalDial(latitude, stylusLength float64) PlanarDial {
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return PlanarDial{
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Latitude: latitude,
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PlaneNormalAzimuth: 180,
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PlaneNormalZenithDistance: 0,
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StylusLength: stylusLength,
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}
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}
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// VerticalDial 垂直日晷 / vertical dial.
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//
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// planeNormalAzimuth 为盘面法线方位角，按正北为 0°、向东增加。
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// 例如：朝南墙面取 180°，朝东墙面取 90°。
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func VerticalDial(latitude, planeNormalAzimuth, stylusLength float64) PlanarDial {
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return PlanarDial{
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Latitude: latitude,
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PlaneNormalAzimuth: normalize360(planeNormalAzimuth),
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PlaneNormalZenithDistance: 90,
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StylusLength: stylusLength,
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}
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}
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// Geometry 返回平面日晷的中心与极轴晷针几何量 / returns the derived planar geometry.
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func (dial PlanarDial) Geometry() PlanarGeometry {
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geometry := PlanarGeometry{
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CenterX: math.NaN(),
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CenterY: math.NaN(),
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PolarStylusLength: math.NaN(),
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PolarStylusPlaneAngle: math.NaN(),
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}
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if !dial.isFinite() {
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return geometry
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}
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P, _, _, _ := dial.baseCoefficients(0, 0)
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geometry.PolarStylusPlaneAngle = math.Asin(clampUnit(math.Abs(P))) * 180 / math.Pi
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if nearZero(P) {
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return geometry
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}
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latSin, latCos := sinCosDeg(dial.Latitude)
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zedSin, zedCos := sinCosDeg(dial.PlaneNormalZenithDistance)
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declinationSin, declinationCos := sinCosDeg(dial.bookPlaneNormalAzimuth())
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geometry.CenterX = dial.StylusLength / P * latCos * declinationSin
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geometry.CenterY = -dial.StylusLength / P * (latSin*zedSin + latCos*zedCos*declinationCos)
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geometry.PolarStylusLength = dial.StylusLength / math.Abs(P)
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geometry.HasFiniteCenter = true
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return geometry
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}
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// ShadowPointByHourAngleDeclination 影尖坐标（按时角与赤纬） / shadow point from hour angle and declination.
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//
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// hourAngle 为有符号太阳时角，上午为负，下午为正；declination 为太阳赤纬，单位度。
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func (dial PlanarDial) ShadowPointByHourAngleDeclination(hourAngle, declination float64) PlanarShadowPoint {
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point := PlanarShadowPoint{
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X: math.NaN(),
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Y: math.NaN(),
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DenominatorQ: math.NaN(),
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}
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if !dial.isFinite() || !isFinite(hourAngle) || !isFinite(declination) {
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return point
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}
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_, Q, Nx, Ny := dial.baseCoefficients(hourAngle, declination)
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point.DenominatorQ = Q
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point.SunAboveHorizon = sunAboveHorizon(hourAngle, declination, dial.Latitude)
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point.PlaneIlluminated = Q > 0
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point.Illuminated = point.SunAboveHorizon && point.PlaneIlluminated
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if nearZero(Q) {
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return point
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}
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point.X = dial.StylusLength * Nx / Q
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point.Y = dial.StylusLength * Ny / Q
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return point
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}
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// ShadowPointAt 影尖坐标（按绝对时刻） / shadow point at an instant.
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//
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// 直接读取该时刻对应的视太阳时角和瞬时太阳赤纬，并返回平面日晷上的影尖位置。
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func (dial PlanarDial) ShadowPointAt(date time.Time, lon float64) PlanarShadowPoint {
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return dial.ShadowPointByHourAngleDeclination(HourAngle(date, lon), sun.ApparentDec(date))
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}
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// MeanSolarTimePoint 平太阳时影尖位置 / shadow point for local mean solar time.
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//
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// date 应处于目标地点的地方平太阳时区，例如 `MeanSolarTime` 的返回值；其原有钟面时间会被忽略。
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// meanSolarHours 为地方平太阳时钟面读数，单位小时，例如 9.5 表示 09:30。
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func (dial PlanarDial) MeanSolarTimePoint(date time.Time, meanSolarHours float64) PlanarShadowPoint {
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sampleTime := dateWithClockHours(date, meanSolarHours)
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declination := sun.ApparentDec(sampleTime)
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return dial.ShadowPointByHourAngleDeclination(MeanSolarHourAngle(sampleTime, meanSolarHours), declination)
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}
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// ZoneTimePoint 区时影尖位置 / shadow point for zone time.
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//
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// date 提供民用日期和时区，原有钟面时间会被忽略；zoneTimeHours 为该时区下的区时钟面读数。
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func (dial PlanarDial) ZoneTimePoint(date time.Time, lon, zoneTimeHours float64) PlanarShadowPoint {
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sampleTime := dateWithClockHours(date, zoneTimeHours)
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declination := sun.ApparentDec(sampleTime)
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return dial.ShadowPointByHourAngleDeclination(HourAngle(sampleTime, lon), declination)
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}
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// MeanSolarTimeLine 平太阳时时间线 / local mean solar time line.
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//
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// dates 由调用者自行决定取样日期密度，例如每月或每日；每个 date 都应处于目标地点的地方平太阳时区，
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// 例如先通过 `MeanSolarTime` 得到对应地点的地方平太阳时再取其年月日。meanSolarHours 为地方平太阳时钟面读数。
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func (dial PlanarDial) MeanSolarTimeLine(dates []time.Time, meanSolarHours float64) []TimeLineSample {
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if !isFinite(meanSolarHours) {
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return nil
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}
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samples := make([]TimeLineSample, 0, len(dates))
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for _, date := range dates {
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sampleTime := dateWithClockHours(date, meanSolarHours)
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declination := sun.ApparentDec(sampleTime)
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hourAngle := MeanSolarHourAngle(sampleTime, meanSolarHours)
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samples = append(samples, TimeLineSample{
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Date: sampleTime,
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Declination: declination,
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HourAngle: hourAngle,
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Point: dial.ShadowPointByHourAngleDeclination(hourAngle, declination),
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})
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}
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return samples
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}
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// ZoneTimeLine 区时时间线 / zone-time line.
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//
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// dates 由调用者自行决定取样日期密度；zoneTimeHours 为 date 所在时区的区时钟面读数。
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// 每个 date 的原有钟面时间都会被 zoneTimeHours 替换。
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func (dial PlanarDial) ZoneTimeLine(dates []time.Time, lon, zoneTimeHours float64) []TimeLineSample {
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if !isFinite(zoneTimeHours) || !isFinite(lon) {
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return nil
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}
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samples := make([]TimeLineSample, 0, len(dates))
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for _, date := range dates {
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sampleTime := dateWithClockHours(date, zoneTimeHours)
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declination := sun.ApparentDec(sampleTime)
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hourAngle := HourAngle(sampleTime, lon)
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samples = append(samples, TimeLineSample{
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Date: sampleTime,
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Declination: declination,
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HourAngle: hourAngle,
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Point: dial.ShadowPointByHourAngleDeclination(hourAngle, declination),
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})
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}
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return samples
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}
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// PlaneIlluminatedHourAngleIntervals 盘面受光时角区间 / plane-illuminated hour-angle intervals.
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//
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// declination 为太阳赤纬，单位度。返回的区间只考虑盘面受光，不判断太阳是否在地平线上方。
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func (dial PlanarDial) PlaneIlluminatedHourAngleIntervals(declination float64) []HourAngleInterval {
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if !dial.isFinite() || !isFinite(declination) {
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return nil
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}
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sinCoeff, cosCoeff, constant := dial.qCoefficients(declination)
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return positiveHourAngleIntervals(sinCoeff, cosCoeff, constant)
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}
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// IlluminatedHourAngleIntervals 可见且受光时角区间 / illuminated hour-angle intervals.
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//
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// declination 为太阳赤纬，单位度。结果可直接用于日晷绘图时筛掉无效时线。
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func (dial PlanarDial) IlluminatedHourAngleIntervals(declination float64) []HourAngleInterval {
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aboveHorizon := SunAboveHorizonHourAngleIntervals(dial.Latitude, declination)
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planeLit := dial.PlaneIlluminatedHourAngleIntervals(declination)
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return intersectHourAngleIntervals(aboveHorizon, planeLit)
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}
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// DeclinationCurve 赤纬曲线采样 / declination-curve samples.
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//
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// declination 为太阳赤纬，单位度；hourAngleStep 为采样步长，单位度，常用值是 15°（每小时一格）。
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// 返回值按受光区间分段，每段都带有精确的时角范围；Samples 只包含区间内部的有效采样点。
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func (dial PlanarDial) DeclinationCurve(declination, hourAngleStep float64) []DeclinationCurveSegment {
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if !dial.isFinite() || !isFinite(declination) || !isFinite(hourAngleStep) || hourAngleStep <= 0 {
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return nil
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}
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intervals := dial.IlluminatedHourAngleIntervals(declination)
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segments := make([]DeclinationCurveSegment, 0, len(intervals))
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for _, interval := range intervals {
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sampleAngles := intervalInteriorSampleAngles(interval, hourAngleStep)
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samples := make([]DeclinationCurveSample, 0, len(sampleAngles))
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for _, hourAngle := range sampleAngles {
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samples = append(samples, DeclinationCurveSample{
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HourAngle: hourAngle,
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Point: dial.ShadowPointByHourAngleDeclination(hourAngle, declination),
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})
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}
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segments = append(segments, DeclinationCurveSegment{
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Declination: declination,
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Interval: interval,
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Samples: samples,
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})
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}
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return segments
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}
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// DeclinationCurveAt 瞬时赤纬曲线采样 / declination-curve samples at an instant.
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//
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// 用 date 对应瞬时太阳赤纬生成日晷分段曲线采样。
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func (dial PlanarDial) DeclinationCurveAt(date time.Time, hourAngleStep float64) []DeclinationCurveSegment {
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return dial.DeclinationCurve(sun.ApparentDec(date), hourAngleStep)
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}
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// SunAboveHorizonHourAngleIntervals 地平线上方时角区间 / above-horizon hour-angle intervals.
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//
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// latitude 为地理纬度，declination 为太阳赤纬，单位度。结果只反映太阳是否升到地平线上方，
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// 不包含盘面朝向的影响。
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func SunAboveHorizonHourAngleIntervals(latitude, declination float64) []HourAngleInterval {
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if !isFinite(latitude) || !isFinite(declination) {
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return nil
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}
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latRad := latitude * math.Pi / 180
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declinationRad := declination * math.Pi / 180
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threshold := -math.Tan(latRad) * math.Tan(declinationRad)
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if threshold <= -1 {
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return fullDayHourAngleIntervals()
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}
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if threshold >= 1 {
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return nil
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}
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halfWidth := math.Acos(clampUnit(threshold)) * 180 / math.Pi
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if nearZero(halfWidth) {
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return nil
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}
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return []HourAngleInterval{{Start: -halfWidth, End: halfWidth}}
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}
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func (dial PlanarDial) baseCoefficients(hourAngle, declination float64) (P, Q, Nx, Ny float64) {
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latSin, latCos := sinCosDeg(dial.Latitude)
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zedSin, zedCos := sinCosDeg(dial.PlaneNormalZenithDistance)
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declinationSin, declinationCos := sinCosDeg(dial.bookPlaneNormalAzimuth())
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hourAngleSin, hourAngleCos := sinCosDeg(hourAngle)
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declinationTan := math.Tan(declination * math.Pi / 180)
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P = latSin*zedCos - latCos*zedSin*declinationCos
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Q = declinationSin*zedSin*hourAngleSin +
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(latCos*zedCos+latSin*zedSin*declinationCos)*hourAngleCos +
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P*declinationTan
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Nx = declinationCos*hourAngleSin -
|
||||
declinationSin*(latSin*hourAngleCos-latCos*declinationTan)
|
||||
Ny = zedCos*declinationSin*hourAngleSin -
|
||||
(latCos*zedSin-latSin*zedCos*declinationCos)*hourAngleCos -
|
||||
(latSin*zedSin+latCos*zedCos*declinationCos)*declinationTan
|
||||
return P, Q, Nx, Ny
|
||||
}
|
||||
|
||||
func (dial PlanarDial) bookPlaneNormalAzimuth() float64 {
|
||||
return normalize360(dial.PlaneNormalAzimuth - 180)
|
||||
}
|
||||
|
||||
func (dial PlanarDial) qCoefficients(declination float64) (sinCoeff, cosCoeff, constant float64) {
|
||||
latSin, latCos := sinCosDeg(dial.Latitude)
|
||||
zedSin, zedCos := sinCosDeg(dial.PlaneNormalZenithDistance)
|
||||
declinationSin, declinationCos := sinCosDeg(dial.bookPlaneNormalAzimuth())
|
||||
P := latSin*zedCos - latCos*zedSin*declinationCos
|
||||
return declinationSin * zedSin,
|
||||
latCos*zedCos + latSin*zedSin*declinationCos,
|
||||
P * math.Tan(declination*math.Pi/180)
|
||||
}
|
||||
|
||||
func (dial PlanarDial) isFinite() bool {
|
||||
return isFinite(dial.Latitude) &&
|
||||
isFinite(dial.PlaneNormalAzimuth) &&
|
||||
isFinite(dial.PlaneNormalZenithDistance) &&
|
||||
isFinite(dial.StylusLength)
|
||||
}
|
||||
|
||||
func sunAboveHorizon(hourAngle, declination, latitude float64) bool {
|
||||
latSin, latCos := sinCosDeg(latitude)
|
||||
decSin, decCos := sinCosDeg(declination)
|
||||
_, hourAngleCos := sinCosDeg(hourAngle)
|
||||
return latSin*decSin+latCos*decCos*hourAngleCos > 0
|
||||
}
|
||||
|
||||
func sinCosDeg(value float64) (sinValue, cosValue float64) {
|
||||
rad := value * math.Pi / 180
|
||||
return math.Sin(rad), math.Cos(rad)
|
||||
}
|
||||
|
||||
func normalize360(value float64) float64 {
|
||||
value = math.Mod(value, 360)
|
||||
if value < 0 {
|
||||
value += 360
|
||||
}
|
||||
return value
|
||||
}
|
||||
|
||||
func clampUnit(value float64) float64 {
|
||||
if value > 1 {
|
||||
return 1
|
||||
}
|
||||
if value < -1 {
|
||||
return -1
|
||||
}
|
||||
return value
|
||||
}
|
||||
|
||||
func nearZero(value float64) bool {
|
||||
return math.Abs(value) <= 1e-15
|
||||
}
|
||||
|
||||
func positiveHourAngleIntervals(sinCoeff, cosCoeff, constant float64) []HourAngleInterval {
|
||||
radius := math.Hypot(sinCoeff, cosCoeff)
|
||||
if nearZero(radius) {
|
||||
if constant > 0 {
|
||||
return fullDayHourAngleIntervals()
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
threshold := -constant / radius
|
||||
if threshold <= -1 {
|
||||
return fullDayHourAngleIntervals()
|
||||
}
|
||||
if threshold >= 1 {
|
||||
return nil
|
||||
}
|
||||
|
||||
center := math.Atan2(sinCoeff, cosCoeff) * 180 / math.Pi
|
||||
halfWidth := math.Acos(clampUnit(threshold)) * 180 / math.Pi
|
||||
if nearZero(halfWidth) {
|
||||
return nil
|
||||
}
|
||||
return splitWrappedSignedInterval(center-halfWidth, center+halfWidth)
|
||||
}
|
||||
|
||||
func splitWrappedSignedInterval(start, end float64) []HourAngleInterval {
|
||||
if end-start >= 360-negligibleHourAngle {
|
||||
return fullDayHourAngleIntervals()
|
||||
}
|
||||
for start < -180 {
|
||||
start += 360
|
||||
end += 360
|
||||
}
|
||||
for start >= 180 {
|
||||
start -= 360
|
||||
end -= 360
|
||||
}
|
||||
if end <= 180 {
|
||||
return []HourAngleInterval{{Start: start, End: end}}
|
||||
}
|
||||
return []HourAngleInterval{
|
||||
{Start: -180, End: end - 360},
|
||||
{Start: start, End: 180},
|
||||
}
|
||||
}
|
||||
|
||||
func intersectHourAngleIntervals(a, b []HourAngleInterval) []HourAngleInterval {
|
||||
if len(a) == 0 || len(b) == 0 {
|
||||
return nil
|
||||
}
|
||||
intersections := make([]HourAngleInterval, 0, len(a)+len(b))
|
||||
for i, j := 0, 0; i < len(a) && j < len(b); {
|
||||
start := math.Max(a[i].Start, b[j].Start)
|
||||
end := math.Min(a[i].End, b[j].End)
|
||||
if end-start > negligibleHourAngle {
|
||||
intersections = append(intersections, HourAngleInterval{Start: start, End: end})
|
||||
}
|
||||
switch {
|
||||
case a[i].End < b[j].End-negligibleHourAngle:
|
||||
i++
|
||||
case b[j].End < a[i].End-negligibleHourAngle:
|
||||
j++
|
||||
default:
|
||||
i++
|
||||
j++
|
||||
}
|
||||
}
|
||||
return intersections
|
||||
}
|
||||
|
||||
func intervalInteriorSampleAngles(interval HourAngleInterval, step float64) []float64 {
|
||||
if !isFinite(interval.Start) || !isFinite(interval.End) || !isFinite(step) || step <= 0 {
|
||||
return nil
|
||||
}
|
||||
if interval.End-interval.Start <= negligibleHourAngle {
|
||||
return nil
|
||||
}
|
||||
|
||||
samples := make([]float64, 0, int(math.Ceil((interval.End-interval.Start)/step)))
|
||||
first := math.Ceil((interval.Start+negligibleHourAngle)/step) * step
|
||||
for hourAngle := first; hourAngle < interval.End-negligibleHourAngle; hourAngle += step {
|
||||
samples = append(samples, hourAngle)
|
||||
}
|
||||
if len(samples) == 0 {
|
||||
samples = append(samples, (interval.Start+interval.End)/2)
|
||||
}
|
||||
return samples
|
||||
}
|
||||
|
||||
func fullDayHourAngleIntervals() []HourAngleInterval {
|
||||
return []HourAngleInterval{{Start: -180, End: 180}}
|
||||
}
|
||||
|
||||
const negligibleHourAngle = 1e-12
|
||||
Reference in New Issue
Block a user