fix: Fortran engine use_marker/alpha header passthrough + case04 Moon orbit fix

- engines/fortran/main.f90:
  - 新增 use_marker 和 alpha_str 的读取、传递、写入 display.txt header
  - 新增 json_get_alpha 函数兼容 JSON 单值或 6 元数组
- engines/release/: 引擎校准缓存 & fortran.json 参数
- examples/case04/: 修正月球位置 (11.5→10.5) 和速度 (526→647),
  地月距缩至希尔半径以内 (0.5 < 1.0), 新增希尔半径验证说明
- examples/Readme.html: case04/case09 描述更新

engines/fortran/main.f90

@@ -21,6 +21,8 @@ program dynamics_f90
     integer :: driving_force
     double precision :: gravity_strength
     character(len=32) :: method
+    integer :: use_marker
+    character(len=512) :: alpha_str
     double precision :: t0, t1, elapsed, tw
 
     ! 原子数据
@@ -71,7 +73,8 @@ program dynamics_f90
     ! 读取 param.json
     call read_params(param_path, box_a, NT, DT, NSTEP, warmup_steps, method, G, B, &
                      gravity_field, gravity_interaction, &
-                     elastic_force, damping_force, gravity_strength, driving_force)
+                     elastic_force, damping_force, gravity_strength, driving_force, &
+                     use_marker, alpha_str)
 
     ! 读取 coord.txt
     call read_coord(input_dir, n_atoms, atom_ids, masses, radii, pos_0, vel_0, fixed)
@@ -201,7 +204,8 @@ program dynamics_f90
                            traj_x, traj_y, traj_z, traj_vx, traj_vy, traj_vz, &
                            NT, DT, NSTEP, warmup_steps, method, G, B, &
                            n_bonds, gravity_field, elastic_force, damping_force, &
-                           driving_force, box_a, gravity_strength)
+                           driving_force, box_a, gravity_strength, &
+                           use_marker, alpha_str)
 
     call cpu_time(t1)
     elapsed = t1 - t0
@@ -228,15 +232,17 @@ contains
 ! ========================================================================
 subroutine read_params(path, box_a, NT, DT, NSTEP, warmup_steps, method, G, B, &
                        gravity_field, gravity_interaction, &
-                       elastic_force, damping_force, gravity_strength, driving_force)
+                       elastic_force, damping_force, gravity_strength, driving_force, &
+                       use_marker, alpha_str)
     character(len=*), intent(in) :: path
     double precision, intent(out) :: box_a, DT, G(3), B(3), gravity_strength
     integer, intent(out) :: NT, NSTEP, warmup_steps
     integer, intent(out) :: gravity_field, gravity_interaction, elastic_force, damping_force, driving_force
-    character(len=*), intent(out) :: method
+    integer, intent(out) :: use_marker
+    character(len=*), intent(out) :: method, alpha_str
     character(len=8096) :: buf
     character(len=256) :: line
-    integer :: u, ios
+    integer :: u, ios, i
 
     box_a = 10.0d0; NT = 10000; DT = 0.001d0; NSTEP = 100; warmup_steps = 0
     method = 'leapfrog'
@@ -244,6 +250,8 @@ subroutine read_params(path, box_a, NT, DT, NSTEP, warmup_steps, method, G, B, &
     gravity_field = 1; gravity_interaction = 0
     elastic_force = 1; damping_force = 0; gravity_strength = 1.0d0
     driving_force = 0
+    use_marker = 0
+    alpha_str = '0.2'
 
     open(newunit=u, file=trim(path), status='old', action='read', iostat=ios)
     if (ios /= 0) then
@@ -274,6 +282,8 @@ subroutine read_params(path, box_a, NT, DT, NSTEP, warmup_steps, method, G, B, &
     damping_force       = json_get_int(buf, 'damping_force', 0)
     gravity_strength    = json_get_double(buf, 'gravity_strength', 1.0d0)
     driving_force       = json_get_int(buf, 'driving_force', 0)
+    use_marker          = json_get_int(buf, 'use_marker', 0)
+    call json_get_alpha(buf, 'alpha', alpha_str)
 end subroutine read_params
 
 ! ========================================================================
@@ -323,6 +333,55 @@ subroutine json_get_double3(buf, key, vals)
     end do
 end subroutine json_get_double3
 
+! 读取 alpha：兼容单值 (0.2) 或 6 元数组 [0.0,0.0,0.0,0.0,0.0,0.0]
+! 输出为逗号分隔字符串，与 draw.py 的解析格式一致
+subroutine json_get_alpha(buf, key, val)
+    character(len=*), intent(in) :: buf, key
+    character(len=*), intent(out) :: val
+    double precision :: d6(6)
+    integer :: p, i, ios
+    character(len=32) :: tmp
+    val = '0.2'
+    p = index(buf, '"' // key // '"')
+    if (p == 0) return
+    p = index(buf(p:), ':') + p
+    ! skip whitespace
+    do while (p <= len(buf) .and. (buf(p:p) == ':' .or. buf(p:p) == ' ' &
+           .or. buf(p:p) == char(9) .or. buf(p:p) == char(10)))
+        p = p + 1
+    end do
+    if (buf(p:p) == '[') then
+        ! 6 元数组
+        d6 = 0.2d0
+        p = p + 1
+        do i = 1, 6
+            do while (p <= len(buf) .and. (buf(p:p) == ' ' .or. buf(p:p) == ',' &
+                   .or. buf(p:p) == char(9) .or. buf(p:p) == char(10)))
+                p = p + 1
+            end do
+            if (p > len(buf) .or. buf(p:p) == ']') exit
+            read(buf(p:), *, iostat=ios) d6(i)
+            if (ios /= 0) exit
+            do while (p <= len(buf) .and. buf(p:p) /= ',' .and. buf(p:p) /= ']')
+                p = p + 1
+            end do
+        end do
+        val = ''
+        do i = 1, 6
+            write(tmp, '(f0.6)') d6(i)
+            if (i > 1) val = trim(val) // ','
+            val = trim(val) // trim(tmp)
+        end do
+    else
+        ! 单值标量
+        read(buf(p:), *, iostat=ios) d6(1)
+        if (ios == 0) then
+            write(tmp, '(f0.6)') d6(1)
+            val = trim(tmp)
+        end if
+    end if
+end subroutine json_get_alpha
+
 ! 从 JSON 中读取字符串值
 subroutine json_get_string(buf, key, val)
     character(len=*), intent(in) :: buf, key
@@ -999,10 +1058,12 @@ subroutine write_display_txt(outdir, n_frames, nat, aid, &
                               tx, ty, tz, tvx, tvy, tvz, &
                               NT, DT, NSTEP, warmup, method, G, B, &
                               nb, gravity_field, elastic_force, damping_force, &
-                              driving_force, box_a, gravity_strength)
-    character(len=*), intent(in) :: outdir, method
+                              driving_force, box_a, gravity_strength, &
+                              use_marker, alpha_str)
+    character(len=*), intent(in) :: outdir, method, alpha_str
     integer, intent(in) :: n_frames, nat, NT, NSTEP, warmup, nb
     integer, intent(in) :: gravity_field, elastic_force, damping_force, driving_force
+    integer, intent(in) :: use_marker
     integer, intent(in) :: aid(nat)
     double precision, intent(in) :: tx(n_frames, nat), ty(n_frames, nat), tz(n_frames, nat)
     double precision, intent(in) :: tvx(n_frames, nat), tvy(n_frames, nat), tvz(n_frames, nat)
@@ -1051,6 +1112,8 @@ subroutine write_display_txt(outdir, n_frames, nat, aid, &
     write(buf, '("Y_MAX: ", g0)')  box_a;  write(u, '(a)') trim(buf)
     write(buf, '("Z_MIN: ", g0)') -box_a;  write(u, '(a)') trim(buf)
     write(buf, '("Z_MAX: ", g0)')  box_a;  write(u, '(a)') trim(buf)
+    write(u, '("use_marker: ", i0)')  use_marker
+    write(u, '("alpha: ", a)')         trim(alpha_str)
 
     ! ── frame data ────────────────────────────────────────────────────────
     do f = 1, n_frames

engines/release/_calib_c.json

@@ -1 +1 @@
-{"n_atoms": 40, "nt": 10000, "step_time": 0.00015027170181274412}
+{"n_atoms": 40, "nt": 10000, "step_time": 3.113259077072144e-05}

engines/release/_calib_fortran.json

@@ -0,0 +1 @@
+{"n_atoms": 40, "nt": 200000, "step_time": 0.0002908185601234436}

engines/release/fortran.json

@@ -0,0 +1,51 @@
+{
+  "box_a": 300.0,
+  "NT": 200000,
+  "DT": 0.001,
+  "NSTEP": 100,
+  "warmup_steps": 0,
+  "method": "leapfrog",
+  "G": [
+    0.0,
+    0.0,
+    0.0
+  ],
+  "B": [
+    0.005,
+    0.0,
+    0.005
+  ],
+  "gravity_field": 0,
+  "gravity_interaction": 0,
+  "elastic_force": 1,
+  "damping_force": 0,
+  "gravity_strength": 1.0,
+  "driving_force": 1,
+  "save_trajectory": 0,
+  "alpha": [
+    0.0,
+    0.0,
+    0.0,
+    0.0,
+    0.0,
+    0.0
+  ],
+  "ball_radius": 0.5,
+  "ball_color": [
+    0.2,
+    0.6,
+    0.9
+  ],
+  "box_color": [
+    0.8,
+    0.8,
+    0.85
+  ],
+  "use_marker": 1,
+  "camera_distance": 60.0,
+  "camera_elevation": 0.0,
+  "camera_azimuth": 0.0,
+  "camera_center_x": 30.0,
+  "camera_center_y": 0.0,
+  "camera_center_z": 0.0
+}