### Question

## How can I determine the tilt angle of a plane given an X Angle and Y Angle from the Surface Plane tool?

### Answer

Sensor Model | G2xxx, G3xxx |

Firmware Version | All |

SDK Version | n/a |

The tilt angle is defined here as the angle between the X-Y plane and the plane measured with the Surface Plane tool.

The tilt angle can also be understood as the angle between the Z axis and the surface normal vector. This allows us to calculate the angle from the dot product of these two vectors. The dot product of the Z axis unit vector and the surface normal is equal to the Z component of the surface normal vector, which is cos(X_Angle) * cos(Y_Angle). The tilt angle can be calculated from the arc-cosine of this value:

tilt = acos(cos(X_Angle) * cos(Y_Angle))

This calculation can be performed in a script, assuming you have added a Surface Plane tool with the default name.

// Gocator script to calculate Surface Plane tilt angle from X and Y Angles. // This script assumes you have Surface Plane tool added with the default name. char* toolName = "Surface Plane"; char* xAngleName = "X Angle"; char* yAngleName = "Y Angle"; float degToRad = 3.141593/180; float radToDeg = 180/3.141593; // check if the measurement tool exists if (Measurement_NameExists(toolName, xAngleName) && Measurement_NameExists(toolName, yAngleName)) { // get the X and Y Angle outputs from the tool and convert to radians float xAngle = degToRad*Measurement_Value(Measurement_Id(toolName, xAngleName)); float yAngle = degToRad*Measurement_Value(Measurement_Id(toolName, yAngleName)); // calculate the tilt in radians float tiltRad = acos(cos(xAngle)*cos(yAngle)); // set the output Output_SetAt(0, tiltRad*radToDeg, 1); } else { // set the output to 0 with a measurement failed decision value Output_SetAt(0, 0, 0); }

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