b612
2bf8478639
- 新增日月食中心带、偏食带、阴影足迹、等时线、食分线及升落边界计算，支持极区与混合食拓扑 - 新增日食单时刻阴影求解器、站心状态查询、批量采样和 ΔT 覆盖接口 - 重构恒星与行星月掩路径，补充有限盘面接触、站心修正、掩带宽度、极区投影及升落边界 - 扩展 SVG 与 GeoJSON 输出，支持详细面板、全球/极区/地球投影、边界闭合、时间标记和拓扑签名 - 扩展日月食候选搜索、局地搜索、沙罗序列预计算与范围外推，补充系列锚点和成员一致性校验 - 补齐古历纪年、儒略历独有闰日、多公历候选、历法改革跨日及精确日期运算接口 - 优化 ΔT、章动、恒星时、月球地平线、事件根搜索和本地星历缓存，降低重复计算开销并提升边界稳定
625 lines
22 KiB
Go
625 lines
22 KiB
Go
package basic
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import (
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"math"
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"sort"
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)
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func solarEclipsePathSampleTimes(startJDE, endJDE, greatestJDE, requestedStepDays float64) ([]float64, float64) {
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return solarEclipseMovingDiskEngine().sampleTimes(
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startJDE, endJDE, greatestJDE, requestedStepDays,
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)
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}
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type solarEclipseRiseSetCurveKey struct {
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phase RiseSetPhase
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direction RiseSetDirection
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}
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type solarEclipseRiseSetTrack struct {
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segments [][]SolarEclipsePathPoint
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}
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type solarEclipseRiseSetEvaluation struct {
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jd float64
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center localSolarEclipseStateContext
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before localSolarEclipseStateContext
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after localSolarEclipseStateContext
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}
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type solarEclipseRiseSetSample struct {
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point SolarEclipsePathPoint
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key solarEclipseRiseSetCurveKey
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}
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type solarEclipseRiseSetPhaseJunction struct {
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point SolarEclipsePathPoint
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direction RiseSetDirection
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}
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type solarEclipseRiseSetSamplePair struct {
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first solarEclipseRiseSetSample
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second solarEclipseRiseSetSample
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}
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func (solver solarEclipseSolver) riseSetCurves(
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startJDE, endJDE, greatestJDE, requestedStepDays float64,
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) []SolarEclipseRiseSetCurve {
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curves, _ := solver.riseSetCurvesWithStatus(startJDE, endJDE, greatestJDE, requestedStepDays)
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return curves
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}
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// riseSetCurvesWithStatus 额外报告六类边界的拓扑校验结果：段数超过每曲线 16 段或用尽
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// 32 段总预算时返回的是截断结果，调用方必须显式标记降级而不是当作完整拓扑。
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func (solver solarEclipseSolver) riseSetCurvesWithStatus(
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startJDE, endJDE, greatestJDE, requestedStepDays float64,
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) ([]SolarEclipseRiseSetCurve, bool) {
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if startJDE == 0 || endJDE == 0 || endJDE <= startJDE {
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return nil, true
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}
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solver = solver.withLocalEphemeris()
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traceStepDays := requestedStepDays
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curves, phaseJunctions, traceStepDays := solver.sampleRiseSetCurves(
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startJDE, endJDE, greatestJDE, traceStepDays,
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)
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topologyStepDays := math.Max(traceStepDays, solarEclipseRiseSetCriticalStepDays)
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// The sampled horizon already contains the complete six-key topology for
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// ordinary events. Running the continuation tracer in that case can split a
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// polar branch into hundreds of tiny components when its tangent changes
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// sign near a fold. Close the sampled endpoints first; only invoke the
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// expensive continuation path if the bounded raw topology cannot be closed.
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if solarEclipseRiseSetRawTopologyUsable(curves) {
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solver.finalizeRiseSetCurveTopology(curves, topologyStepDays, phaseJunctions)
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if solarEclipseRiseSetCurveTopologyComplete(curves) {
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if requestedStepDays > traceStepDays {
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decimateSolarEclipseRiseSetCurves(curves, requestedStepDays)
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}
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return curves, true
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}
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}
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traced := solver.traceRiseSetCurveTopology(curves, startJDE, endJDE, greatestJDE)
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if len(traced) == 6 {
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solver.finalizeRiseSetCurveTopology(traced, topologyStepDays, phaseJunctions)
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}
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if solarEclipseRiseSetCurveTopologyComplete(traced) {
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curves = traced
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} else {
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for _, retryStepDays := range []float64{20.0 / 86400.0, 5.0 / 86400.0} {
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if retryStepDays >= traceStepDays {
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continue
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}
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curves, phaseJunctions, traceStepDays = solver.sampleRiseSetCurves(
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startJDE, endJDE, greatestJDE, retryStepDays,
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)
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topologyStepDays = math.Max(traceStepDays, solarEclipseRiseSetCriticalStepDays)
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retryTraced := solver.traceRiseSetCurveTopology(curves, startJDE, endJDE, greatestJDE)
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if len(retryTraced) == 6 {
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solver.finalizeRiseSetCurveTopology(retryTraced, topologyStepDays, phaseJunctions)
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}
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if solarEclipseRiseSetCurveTopologyComplete(retryTraced) {
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curves = retryTraced
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break
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}
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solver.finalizeRiseSetCurveTopology(curves, topologyStepDays, phaseJunctions)
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if solarEclipseRiseSetCurveTopologyComplete(curves) {
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break
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}
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}
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if !solarEclipseRiseSetCurveTopologyComplete(curves) {
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solver.finalizeRiseSetCurveTopology(curves, topologyStepDays, phaseJunctions)
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}
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}
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if requestedStepDays > traceStepDays {
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decimateSolarEclipseRiseSetCurves(curves, requestedStepDays)
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}
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return curves, solarEclipseRiseSetCurveTopologyComplete(curves)
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}
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func solarEclipseRiseSetRawTopologyUsable(curves []SolarEclipseRiseSetCurve) bool {
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if len(curves) != 6 {
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return false
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}
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seen := make(map[solarEclipseRiseSetCurveKey]bool, 6)
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segments := 0
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for _, curve := range curves {
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key := solarEclipseRiseSetCurveKey{phase: curve.Phase, direction: curve.Direction}
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if seen[key] || len(curve.Segments) == 0 {
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return false
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}
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seen[key] = true
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segments += len(curve.Segments)
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}
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return segments <= 32
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}
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func (solver solarEclipseSolver) sampleRiseSetCurves(
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startJDE, endJDE, greatestJDE, traceStepDays float64,
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) ([]SolarEclipseRiseSetCurve, []solarEclipseRiseSetPhaseJunction, float64) {
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times, traceStepDays := solarEclipsePathSampleTimes(startJDE, endJDE, greatestJDE, traceStepDays)
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keys := []solarEclipseRiseSetCurveKey{
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{RiseSetPhaseStart, RiseSetDirectionRise},
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{RiseSetPhaseStart, RiseSetDirectionSet},
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{RiseSetPhaseGreatest, RiseSetDirectionRise},
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{RiseSetPhaseGreatest, RiseSetDirectionSet},
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{RiseSetPhaseEnd, RiseSetDirectionRise},
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{RiseSetPhaseEnd, RiseSetDirectionSet},
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}
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tracks := make(map[solarEclipseRiseSetCurveKey][]*solarEclipseRiseSetTrack, len(keys))
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var previousContactSamples []solarEclipseRiseSetSample
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var phaseJunctions []solarEclipseRiseSetPhaseJunction
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for _, jd := range times {
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pointsAt := solver.riseSetCandidatePointsAt(jd, solarEclipseRiseSetBoundaryPoints)
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contactSamples := solarEclipseRiseSetContactSamples(pointsAt)
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phaseJunctions = solver.appendRiseSetPhaseJunctionsAtSamples(
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phaseJunctions, contactSamples, traceStepDays,
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)
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phaseJunctions = solver.appendRiseSetPhaseJunctionsBetweenSamples(
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phaseJunctions, previousContactSamples, contactSamples,
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)
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previousContactSamples = contactSamples
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for _, key := range keys {
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tracks[key] = appendSolarEclipseRiseSetSamples(tracks[key], pointsAt[key], traceStepDays)
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}
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}
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curves := make([]SolarEclipseRiseSetCurve, 0, len(keys))
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for _, key := range keys {
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segments := make([][]SolarEclipsePathPoint, 0, len(tracks[key]))
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for _, track := range tracks[key] {
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for _, segment := range track.segments {
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if len(segment) >= 2 {
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segments = append(segments, segment)
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}
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}
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}
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if len(segments) == 0 {
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continue
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}
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curves = append(curves, SolarEclipseRiseSetCurve{
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Phase: key.phase, Direction: key.direction, Segments: segments,
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})
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}
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return curves, phaseJunctions, traceStepDays
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}
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func (solver solarEclipseSolver) finalizeRiseSetCurveTopology(
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curves []SolarEclipseRiseSetCurve,
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topologyStepDays float64,
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phaseJunctions []solarEclipseRiseSetPhaseJunction,
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) {
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solver.completeRiseSetCurveEndpoints(curves, topologyStepDays, phaseJunctions)
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snapSolarEclipseRiseSetArcPhaseJunctions(curves, phaseJunctions)
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solver.closeSolarEclipseRiseSetArcFolds(curves, phaseJunctions)
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solver.snapNearCoincidentSolarEclipseRiseSetEndpoints(curves)
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solver.closeSolarEclipseRiseSetArcDirectionJunctions(curves, phaseJunctions)
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deduplicateSolarEclipseRiseSetArcSegments(curves)
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sortSolarEclipseRiseSetSegments(curves)
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}
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func decimateSolarEclipseRiseSetCurves(
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curves []SolarEclipseRiseSetCurve,
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stepDays float64,
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) {
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for curveIndex := range curves {
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for segmentIndex, segment := range curves[curveIndex].Segments {
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if len(segment) < 3 {
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continue
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}
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decimated := make([]SolarEclipsePathPoint, 1, len(segment))
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decimated[0] = segment[0]
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lastIndex := 0
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for pointIndex := 1; pointIndex < len(segment)-1; pointIndex++ {
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last := decimated[len(decimated)-1]
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next := segment[pointIndex+1]
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if next.JDE-last.JDE <= stepDays+solarEclipseRiseSetTimeEpsilonDays &&
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solarEclipsePathDistanceKM(last, next) <= solarEclipseRiseSetTargetSpacingKM {
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accurate := true
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for _, point := range segment[lastIndex+1 : pointIndex+1] {
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if solarEclipseRiseSetChordDeviationKM(point, last, next) > solarEclipseRiseSetChordToleranceKM {
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accurate = false
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break
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}
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}
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if accurate {
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continue
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}
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}
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decimated = append(decimated, segment[pointIndex])
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lastIndex = pointIndex
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}
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decimated = append(decimated, segment[len(segment)-1])
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curves[curveIndex].Segments[segmentIndex] = decimated
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}
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}
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}
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func solarEclipseRiseSetContactSamples(
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pointsAt map[solarEclipseRiseSetCurveKey][]SolarEclipsePathPoint,
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) []solarEclipseRiseSetSample {
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var samples []solarEclipseRiseSetSample
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for _, phase := range []RiseSetPhase{RiseSetPhaseStart, RiseSetPhaseEnd} {
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for _, direction := range []RiseSetDirection{RiseSetDirectionRise, RiseSetDirectionSet} {
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key := solarEclipseRiseSetCurveKey{phase: phase, direction: direction}
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for _, point := range pointsAt[key] {
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samples = append(samples, solarEclipseRiseSetSample{point: point, key: key})
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}
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}
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}
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return samples
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}
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func (solver solarEclipseSolver) appendRiseSetPhaseJunctionsAtSamples(
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junctions []solarEclipseRiseSetPhaseJunction,
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samples []solarEclipseRiseSetSample,
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stepDays float64,
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) []solarEclipseRiseSetPhaseJunction {
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for firstIndex, first := range samples {
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for secondIndex := firstIndex + 1; secondIndex < len(samples); secondIndex++ {
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second := samples[secondIndex]
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if solarEclipsePathDistanceKM(first.point, second.point) > 1500 {
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continue
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}
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candidate, ok := SolarEclipsePathPoint{}, false
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for _, seed := range []SolarEclipsePathPoint{
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solarEclipseRiseSetMidpoint(first.point, second.point),
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first.point,
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second.point,
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} {
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candidate, ok = solver.refineRiseSetPhaseJunctionOnHorizon(seed)
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if !ok {
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candidate, ok = solver.refineRiseSetPhaseJunction(
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seed.JDE, seed.Longitude, seed.Latitude,
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)
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}
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if ok {
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break
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}
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}
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if !ok || math.Abs(candidate.JDE-first.point.JDE) > stepDays ||
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solarEclipsePathDistanceKM(candidate, first.point) > 3000 ||
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solarEclipsePathDistanceKM(candidate, second.point) > 3000 {
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continue
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}
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junctions = solver.appendRiseSetPhaseJunction(junctions, candidate)
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}
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}
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return junctions
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}
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func (solver solarEclipseSolver) appendRiseSetPhaseJunction(
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junctions []solarEclipseRiseSetPhaseJunction,
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candidate SolarEclipsePathPoint,
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) []solarEclipseRiseSetPhaseJunction {
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evaluation := solver.magnitudeEvaluationAt(candidate.JDE)
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altitudeDerivative := evaluation.sunAltitudeDerivative(candidate.Longitude, candidate.Latitude)
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if !finite(altitudeDerivative) || math.Abs(altitudeDerivative) < 1e-10 {
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return junctions
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}
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direction := RiseSetDirectionSet
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if altitudeDerivative > 0 {
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direction = RiseSetDirectionRise
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}
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for _, junction := range junctions {
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if math.Abs(junction.point.JDE-candidate.JDE) <= solarEclipseRiseSetTimeEpsilonDays &&
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solarEclipsePathDistanceKM(junction.point, candidate) <= 0.01 {
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return junctions
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}
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}
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return append(junctions, solarEclipseRiseSetPhaseJunction{
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point: candidate, direction: direction,
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})
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}
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func (solver solarEclipseSolver) appendRiseSetPhaseJunctionsBetweenSamples(
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junctions []solarEclipseRiseSetPhaseJunction,
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previous, current []solarEclipseRiseSetSample,
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) []solarEclipseRiseSetPhaseJunction {
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if len(previous) == 0 || len(current) == 0 {
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return junctions
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}
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for _, pair := range solarEclipseMatchRiseSetSamples(previous, current) {
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if pair.first.key.phase == pair.second.key.phase {
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continue
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}
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candidate, ok := solver.refineRiseSetPhaseJunctionBetweenSamples(pair.first, pair.second)
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if !ok {
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continue
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}
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if candidate.JDE < pair.first.point.JDE-solarEclipseRiseSetTimeEpsilonDays ||
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candidate.JDE > pair.second.point.JDE+solarEclipseRiseSetTimeEpsilonDays ||
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solarEclipsePathDistanceKM(candidate, pair.first.point) > 6000 ||
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solarEclipsePathDistanceKM(candidate, pair.second.point) > 6000 {
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continue
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}
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junctions = solver.appendRiseSetPhaseJunction(junctions, candidate)
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}
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return junctions
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}
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func solarEclipseMatchRiseSetSamples(
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previous, current []solarEclipseRiseSetSample,
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) []solarEclipseRiseSetSamplePair {
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type candidatePair struct {
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firstIndex int
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secondIndex int
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distance float64
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}
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var candidates []candidatePair
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for firstIndex, first := range previous {
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for secondIndex, second := range current {
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deltaDays := second.point.JDE - first.point.JDE
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distance := solarEclipsePathDistanceKM(first.point, second.point)
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if deltaDays <= 0 || riseSetGeographicBranchChanged(distance, deltaDays) {
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continue
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}
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candidates = append(candidates, candidatePair{
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firstIndex: firstIndex, secondIndex: secondIndex, distance: distance,
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})
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}
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}
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sort.Slice(candidates, func(first, second int) bool {
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return candidates[first].distance < candidates[second].distance
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})
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usedFirst := make([]bool, len(previous))
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usedSecond := make([]bool, len(current))
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var pairs []solarEclipseRiseSetSamplePair
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for _, candidate := range candidates {
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if usedFirst[candidate.firstIndex] || usedSecond[candidate.secondIndex] {
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continue
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}
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usedFirst[candidate.firstIndex] = true
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usedSecond[candidate.secondIndex] = true
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pairs = append(pairs, solarEclipseRiseSetSamplePair{
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first: previous[candidate.firstIndex], second: current[candidate.secondIndex],
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})
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}
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return pairs
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}
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func (solver solarEclipseSolver) refineRiseSetPhaseJunctionBetweenSamples(
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first, second solarEclipseRiseSetSample,
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) (SolarEclipsePathPoint, bool) {
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left, right := first, second
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for iteration := 0; iteration < 8; iteration++ {
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midpoint := solarEclipseRiseSetMidpoint(left.point, right.point)
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midpoint.JDE = (left.point.JDE + right.point.JDE) / 2
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current := solarEclipseRiseSetContactSamples(
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solver.riseSetPointsAt(midpoint.JDE, solarEclipseRiseSetBoundaryPoints),
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)
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bestIndex := -1
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bestDistance := math.Inf(1)
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for index, sample := range current {
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distance := solarEclipsePathDistanceKM(midpoint, sample.point)
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if distance < bestDistance {
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bestIndex, bestDistance = index, distance
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}
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}
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if bestIndex < 0 || bestDistance > 1000 {
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break
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}
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if current[bestIndex].key.phase == left.key.phase {
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left = current[bestIndex]
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} else if current[bestIndex].key.phase == right.key.phase {
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right = current[bestIndex]
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} else {
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break
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}
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}
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for _, seed := range []SolarEclipsePathPoint{
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solarEclipseRiseSetMidpoint(left.point, right.point),
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left.point,
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right.point,
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} {
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candidate, ok := solver.refineRiseSetPhaseJunctionOnHorizon(seed)
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if !ok {
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candidate, ok = solver.refineRiseSetPhaseJunction(
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seed.JDE, seed.Longitude, seed.Latitude,
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)
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}
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if ok {
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return candidate, true
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}
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}
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return SolarEclipsePathPoint{}, false
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}
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func (solver solarEclipseSolver) riseSetPointsAt(
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jd float64,
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boundaryPoints int,
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) map[solarEclipseRiseSetCurveKey][]SolarEclipsePathPoint {
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return solver.riseSetPointsAtEvaluation(jd, boundaryPoints, solver.magnitudeEvaluationAt(jd))
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}
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func (solver solarEclipseSolver) riseSetCandidatePointsAt(
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jd float64,
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boundaryPoints int,
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) map[solarEclipseRiseSetCurveKey][]SolarEclipsePathPoint {
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return solver.riseSetPointsAtEvaluation(jd, boundaryPoints, solver.magnitudeCandidateEvaluationAt(jd))
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}
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func (solver solarEclipseSolver) riseSetPointsAtEvaluation(
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jd float64,
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boundaryPoints int,
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evaluation solarEclipseRiseSetEvaluation,
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|
) map[solarEclipseRiseSetCurveKey][]SolarEclipsePathPoint {
|
|
result := make(map[solarEclipseRiseSetCurveKey][]SolarEclipsePathPoint, 6)
|
|
sun := solarEclipseXYZToLLR(
|
|
evaluation.center.sunXYZ[0], evaluation.center.sunXYZ[1], evaluation.center.sunXYZ[2],
|
|
)
|
|
centerLongitude := normalizeLongitude((sun[0] - evaluation.center.gst) / rad)
|
|
centerLatitude := sun[1] / rad
|
|
|
|
appendRoots := func(greatest bool) {
|
|
valueAt := func(angle float64) (float64, bool) {
|
|
longitude, latitude := riseSetHorizonPoint(centerLongitude, centerLatitude, angle)
|
|
state := evaluation.center.stateAt(longitude*rad, latitude*rad, 0)
|
|
if greatest {
|
|
value := evaluation.separationDerivative(longitude, latitude)
|
|
return value, finite(value)
|
|
}
|
|
value := solarEclipsePartialContactGap(state)
|
|
return value, finite(value)
|
|
}
|
|
for _, angle := range riseSetCyclicRoots(boundaryPoints, valueAt) {
|
|
longitude, latitude := riseSetHorizonPoint(centerLongitude, centerLatitude, angle)
|
|
longitude, latitude, ok := riseSetRefineGeographicRoot(
|
|
longitude,
|
|
latitude,
|
|
func(lon, lat float64) (float64, float64, bool) {
|
|
state := evaluation.center.stateAt(lon*rad, lat*rad, 0)
|
|
first := solarEclipsePartialContactGap(state)
|
|
if greatest {
|
|
first = evaluation.separationDerivative(lon, lat)
|
|
}
|
|
return first, state.sunAltitudeRad, finite(first) && finite(state.sunAltitudeRad)
|
|
},
|
|
)
|
|
if !ok {
|
|
continue
|
|
}
|
|
point, key, valid := evaluation.classify(longitude, latitude, greatest)
|
|
if !valid || solarEclipseRiseSetPointExists(result[key], point) {
|
|
continue
|
|
}
|
|
result[key] = append(result[key], point)
|
|
}
|
|
}
|
|
appendRoots(false)
|
|
appendRoots(true)
|
|
return result
|
|
}
|
|
|
|
func (evaluation solarEclipseRiseSetEvaluation) classify(
|
|
longitude, latitude float64,
|
|
greatest bool,
|
|
) (SolarEclipsePathPoint, solarEclipseRiseSetCurveKey, bool) {
|
|
state := evaluation.center.stateAt(longitude*rad, latitude*rad, 0)
|
|
altitudeDerivative := evaluation.sunAltitudeDerivative(longitude, latitude)
|
|
if !finite(altitudeDerivative) || math.Abs(altitudeDerivative) < 1e-10 {
|
|
return SolarEclipsePathPoint{}, solarEclipseRiseSetCurveKey{}, false
|
|
}
|
|
direction := RiseSetDirectionSet
|
|
if altitudeDerivative > 0 {
|
|
direction = RiseSetDirectionRise
|
|
}
|
|
phase := RiseSetPhaseGreatest
|
|
if greatest {
|
|
if solarEclipsePartialContactGap(state) > 1e-7 ||
|
|
evaluation.separationSecondDerivative(longitude, latitude) <= 0 {
|
|
return SolarEclipsePathPoint{}, solarEclipseRiseSetCurveKey{}, false
|
|
}
|
|
} else {
|
|
contactDerivative := evaluation.partialContactDerivative(longitude, latitude)
|
|
if !finite(contactDerivative) || math.Abs(contactDerivative) < 1e-10 {
|
|
return SolarEclipsePathPoint{}, solarEclipseRiseSetCurveKey{}, false
|
|
}
|
|
phase = RiseSetPhaseEnd
|
|
if contactDerivative < 0 {
|
|
phase = RiseSetPhaseStart
|
|
}
|
|
}
|
|
return SolarEclipsePathPoint{
|
|
JDE: evaluation.jd, Longitude: longitude, Latitude: latitude, SunAltitude: state.sunAltitudeRad / rad,
|
|
}, solarEclipseRiseSetCurveKey{phase: phase, direction: direction}, true
|
|
}
|
|
|
|
func solarEclipsePartialContactGap(state localSolarEclipseState) float64 {
|
|
return state.movingDiskContactState().externalContactGap()
|
|
}
|
|
|
|
func (evaluation solarEclipseRiseSetEvaluation) partialContactDerivative(longitude, latitude float64) float64 {
|
|
before := evaluation.before.stateAt(longitude*rad, latitude*rad, 0)
|
|
after := evaluation.after.stateAt(longitude*rad, latitude*rad, 0)
|
|
return (solarEclipsePartialContactGap(after) - solarEclipsePartialContactGap(before)) /
|
|
(2 * solarEclipseRiseSetDerivativeStepDays)
|
|
}
|
|
|
|
func (evaluation solarEclipseRiseSetEvaluation) partialContactSecondDerivative(longitude, latitude float64) float64 {
|
|
before := evaluation.before.stateAt(longitude*rad, latitude*rad, 0)
|
|
center := evaluation.center.stateAt(longitude*rad, latitude*rad, 0)
|
|
after := evaluation.after.stateAt(longitude*rad, latitude*rad, 0)
|
|
stepSquared := solarEclipseRiseSetDerivativeStepDays * solarEclipseRiseSetDerivativeStepDays
|
|
return (solarEclipsePartialContactGap(after) - 2*solarEclipsePartialContactGap(center) + solarEclipsePartialContactGap(before)) /
|
|
stepSquared
|
|
}
|
|
|
|
func (evaluation solarEclipseRiseSetEvaluation) sunAltitudeDerivative(longitude, latitude float64) float64 {
|
|
before := evaluation.before.stateAt(longitude*rad, latitude*rad, 0).sunAltitudeRad
|
|
after := evaluation.after.stateAt(longitude*rad, latitude*rad, 0).sunAltitudeRad
|
|
return (after - before) / (2 * solarEclipseRiseSetDerivativeStepDays)
|
|
}
|
|
|
|
func (evaluation solarEclipseRiseSetEvaluation) sunAltitudeSecondDerivative(longitude, latitude float64) float64 {
|
|
before := evaluation.before.stateAt(longitude*rad, latitude*rad, 0).sunAltitudeRad
|
|
center := evaluation.center.stateAt(longitude*rad, latitude*rad, 0).sunAltitudeRad
|
|
after := evaluation.after.stateAt(longitude*rad, latitude*rad, 0).sunAltitudeRad
|
|
stepSquared := solarEclipseRiseSetDerivativeStepDays * solarEclipseRiseSetDerivativeStepDays
|
|
return (after - 2*center + before) / stepSquared
|
|
}
|
|
|
|
func (evaluation solarEclipseRiseSetEvaluation) separationDerivative(longitude, latitude float64) float64 {
|
|
before := evaluation.before.stateAt(longitude*rad, latitude*rad, 0).separationSquared
|
|
after := evaluation.after.stateAt(longitude*rad, latitude*rad, 0).separationSquared
|
|
return (after - before) / (2 * solarEclipseRiseSetDerivativeStepDays)
|
|
}
|
|
|
|
func (evaluation solarEclipseRiseSetEvaluation) separationSecondDerivative(longitude, latitude float64) float64 {
|
|
before := evaluation.before.stateAt(longitude*rad, latitude*rad, 0).separationSquared
|
|
center := evaluation.center.stateAt(longitude*rad, latitude*rad, 0).separationSquared
|
|
after := evaluation.after.stateAt(longitude*rad, latitude*rad, 0).separationSquared
|
|
stepSquared := solarEclipseRiseSetDerivativeStepDays * solarEclipseRiseSetDerivativeStepDays
|
|
return (after - 2*center + before) / stepSquared
|
|
}
|
|
|
|
func solarEclipseRiseSetPointExists(points []SolarEclipsePathPoint, candidate SolarEclipsePathPoint) bool {
|
|
for _, point := range points {
|
|
if solarEclipsePathDistanceKM(point, candidate) < 0.01 {
|
|
return true
|
|
}
|
|
}
|
|
return false
|
|
}
|
|
|
|
func appendSolarEclipseRiseSetSamples(
|
|
tracks []*solarEclipseRiseSetTrack,
|
|
points []SolarEclipsePathPoint,
|
|
stepDays float64,
|
|
) []*solarEclipseRiseSetTrack {
|
|
used := make([]bool, len(tracks))
|
|
for _, point := range points {
|
|
bestTrack := -1
|
|
bestDistance := math.Inf(1)
|
|
for index, track := range tracks {
|
|
if used[index] || len(track.segments) == 0 || len(track.segments[len(track.segments)-1]) == 0 {
|
|
continue
|
|
}
|
|
last := track.segments[len(track.segments)-1][len(track.segments[len(track.segments)-1])-1]
|
|
deltaDays := point.JDE - last.JDE
|
|
if deltaDays <= 0 || deltaDays > 2.5*stepDays {
|
|
continue
|
|
}
|
|
distance := solarEclipsePathDistanceKM(last, point)
|
|
if riseSetGeographicBranchChanged(distance, deltaDays) || distance >= bestDistance {
|
|
continue
|
|
}
|
|
bestTrack, bestDistance = index, distance
|
|
}
|
|
if bestTrack < 0 {
|
|
tracks = append(tracks, &solarEclipseRiseSetTrack{segments: [][]SolarEclipsePathPoint{{point}}})
|
|
used = append(used, true)
|
|
continue
|
|
}
|
|
track := tracks[bestTrack]
|
|
track.segments[len(track.segments)-1] = append(track.segments[len(track.segments)-1], point)
|
|
used[bestTrack] = true
|
|
}
|
|
return tracks
|
|
}
|
|
|
|
func riseSetGeographicBranchChanged(distanceKM, deltaDays float64) bool {
|
|
if distanceKM <= 750 {
|
|
return false
|
|
}
|
|
return deltaDays <= 0 || distanceKM/(deltaDays*86400) > 10
|
|
}
|