feat: 完善时标与天象几何计算并扩展输出接口

- 新增时标、ΔT 模型、质心时间与 UT1 支持
- 改进日月食、月掩、行星事件及路径边界计算
- 完善恒星三维自行与动态距离传播
- 扩展 SVG、GeoJSON、KML 输出与底层距离换算工具
- 整理中英文手册、示例资源及回归测试

basic/occultation_contact_rate_test.go

@@ -0,0 +1,80 @@
+package basic
+
+import (
+	"math"
+	"testing"
+	"time"
+)
+
+// 解析速率与中心差分必须给出同一个接触度量导数：点源目标曾把零位置当站心位置，
+// 减掉观测者速度后得到日尺度的假速率，掩带边界因此无法加密。
+// The analytic contact rate must agree with the central difference for every target
+// kind: the point-source branch once treated a zero position as a topocentric vector
+// and produced a spurious diurnal rate that stopped the band boundary from refining.
+func TestOccultationContactRateMatchesCentralDifference(t *testing.T) {
+	const tolerance = 0.01 // 度/日
+	star := hr4799OccultationCoordinateForTest()
+	infinite := star
+	infinite.ParallaxMas = 0
+	parallaxStar := star
+	parallaxStar.ParallaxMas = 10
+	planetConfig, _ := planetOccultationConfigFor(OccultationMercury)
+	planetCache := newPlanetOccultationEventCache(planetConfig)
+
+	starEvaluation := func(coordinate StarCoordinate) func(float64) occultationRiseSetEvaluation {
+		cache := newStarOccultationEventCache(coordinate)
+		return newOccultationRiseSetEvaluationCache(cache.riseSetContextAt).evaluation
+	}
+	cases := []struct {
+		name       string
+		sampleTime time.Time
+		evaluation func(float64) occultationRiseSetEvaluation
+	}{
+		{"point-source star", time.Date(2025, 6, 5, 10, 0, 0, 0, time.UTC), starEvaluation(infinite)},
+		{"finite star", time.Date(2025, 6, 5, 10, 0, 0, 0, time.UTC), starEvaluation(parallaxStar)},
+		{"planet", time.Date(2024, 8, 21, 10, 0, 0, 0, time.UTC), newOccultationRiseSetEvaluationCache(planetCache.riseSetContextAt).evaluation},
+	}
+	sites := [][2]float64{{0, 0}, {115, 33}, {-74, 40}, {179, 80}, {-123, -64}}
+	for _, testCase := range cases {
+		tt := occultationTimeToTT(testCase.sampleTime)
+		evaluation := testCase.evaluation(tt)
+		for _, site := range sites {
+			analytic := evaluation.contactRateAt(site[0], site[1])
+			reference := evaluation.contactDerivative(site[0], site[1])
+			if !finite(analytic) || !finite(reference) {
+				t.Fatalf("%s lon=%g lat=%g: analytic=%g reference=%g", testCase.name, site[0], site[1], analytic, reference)
+			}
+			if math.Abs(analytic-reference) > tolerance {
+				t.Errorf("%s lon=%g lat=%g: analytic=%.6f reference=%.6f degrees/day",
+					testCase.name, site[0], site[1], analytic, reference)
+			}
+		}
+	}
+}
+
+// 无视差恒星的掩带边界必须加密到请求的地面间距：修复前相邻点可达 150 km。
+func TestStarOccultationBandContourSpacing(t *testing.T) {
+	star := hr4799OccultationCoordinateForTest()
+	start := time.Date(2025, 6, 5, 0, 0, 0, 0, time.UTC)
+	paths, err := FindStarOccultationPaths(start, start.Add(24*time.Hour), star,
+		OccultationPathOptions{Step: 5 * time.Minute, TargetSpacingKM: 30, DisableFootprints: true, DisableRiseSet: true})
+	if err != nil {
+		t.Fatal(err)
+	}
+	const limitKM = 45.0
+	sampled := 0
+	for _, path := range paths {
+		for branch, contour := range path.BandContours {
+			for index := 1; index < len(contour); index++ {
+				spacing := occultationPathDistanceKM(contour[index-1], contour[index])
+				sampled++
+				if spacing > limitKM {
+					t.Fatalf("branch %d sample %d: spacing %.3f km exceeds %.0f km", branch, index, spacing, limitKM)
+				}
+			}
+		}
+	}
+	if sampled == 0 {
+		t.Fatal("no band contour samples")
+	}
+}