143 lines
2.7 KiB
Markdown
143 lines
2.7 KiB
Markdown
# RSEM4 angle and XYZ formulas
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本文只说明 `RsLidarDevice` 中 RSEM4 雷达角度、距离与
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`PointCloudCallback` 输出 XYZ 之间的正算和逆算公式。
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代码依据：`Src/RsLidarDevice.cpp::fillRsem4Point()`。
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## 单位约定
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- 原始距离分辨率：`1 unit = 0.005 m`。
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- 公式中的 `distance_m` 单位为米。
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- `PointCloudCallback` 输出的 `X/Y/Z` 单位为毫米。
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- 代码中的角度单位为 `0.01°`，例如 `1300 = 13.00°`。
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- 三角函数计算时需要先把 `0.01°` 转成弧度：
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```text
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angle_rad = angle_deg01 * pi / 18000
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```
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## 角度定义
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水平角：
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```text
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yaw_deg01 = yawBase_deg01 + yawOffset_deg01[ring / 20]
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```
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垂直角：
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```text
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pitch_deg01 = pitchAngle_deg01[ring] + surfacePitchOffset_deg01[surfaceIndex]
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```
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转换成弧度：
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```text
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yaw_rad = yaw_deg01 * pi / 18000
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pitch_rad = pitch_deg01 * pi / 18000
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```
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## 正算公式：angle + distance -> XYZ
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雷达内部先按标准球坐标计算：
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```text
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x0_m = distance_m * cos(pitch_rad) * cos(yaw_rad)
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y0_m = distance_m * cos(pitch_rad) * sin(yaw_rad)
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z0_m = distance_m * sin(pitch_rad)
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```
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再转换成 `PointCloudCallback` 输出坐标：
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```text
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X_mm = -y0_m * 1000
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Y_mm = -z0_m * 1000
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Z_mm = x0_m * 1000
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```
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合并后：
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```text
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X_mm = -distance_m * cos(pitch_rad) * sin(yaw_rad) * 1000
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Y_mm = -distance_m * sin(pitch_rad) * 1000
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Z_mm = distance_m * cos(pitch_rad) * cos(yaw_rad) * 1000
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```
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强度值：
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```text
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intensity = 原始 intensity
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```
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## 逆算公式：XYZ -> angle + distance
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给定 `PointCloudCallback` 输出点：
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```text
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X_mm = point.x
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Y_mm = point.y
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Z_mm = point.z
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```
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距离：
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```text
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range_mm = sqrt(X_mm * X_mm + Y_mm * Y_mm + Z_mm * Z_mm)
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range_m = range_mm / 1000
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```
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水平角：
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```text
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yaw_rad = atan2(-X_mm, Z_mm)
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yaw_deg = yaw_rad * 180 / pi
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```
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如果需要归一化到 `[0, 360)`：
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```text
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if yaw_deg < 0:
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yaw_deg += 360
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```
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垂直角：
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```text
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pitch_rad = asin(-Y_mm / range_mm)
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pitch_deg = pitch_rad * 180 / pi
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```
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转换成代码中的 `0.01°` 单位：
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```text
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yaw_deg01 = yaw_deg * 100
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pitch_deg01 = pitch_deg * 100
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```
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## 反推原始角度
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上面的逆算得到的是已经叠加 DIFOP 标定补偿后的实际出射角。
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如果已知当前点的 `ring`、`surfaceIndex` 和 DIFOP 标定表，则可继续反推：
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```text
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yawBase_deg01 = yaw_deg01 - yawOffset_deg01[ring / 20]
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pitchAngle_deg01[ring] = pitch_deg01 - surfacePitchOffset_deg01[surfaceIndex]
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```
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如果只拿到 XYZ，不知道 `ring`、`surfaceIndex` 和 DIFOP 标定表，则不能唯一反推原始包里的
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`yawAngle`、`pitchAngle` 或 `surfaceId`。
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## 无效点
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当输出点为零点时：
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```text
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X_mm = 0
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Y_mm = 0
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Z_mm = 0
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```
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不能进行角度逆算。零点可能来自距离越界或 `surfaceIndex` 非法。
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