Geometry: add getLinearized(), getCurved()

[dbaston]

TODO:

• Test Z/M handling
• Review / incorporate GDAL tests from ogr_geom.py
• Add support for maximum-deviation tolerance
• C API

[dbaston]

I've updated the C API to provide for manual or automatic conversion between curved and linear geometry types.

Manual conversion

Uses the curve conversion functions GEOSCurveToLine and GEOSLineToCurve.

GEOSCurveToLine is a simplified version of the PostGIS/QGIS ST_CurveToLine. It divides an arc into fixed-angle sections using either a maximum angle or a maximum deviation. The API allows for other tolerance types to be added in the future, as long as they fit the signature of GEOSCurveToLine_setTolerance(int toleranceType, double toleranceValue).

GEOSLineToCurve generally follows PostGIS ST_LineToCurve. It exposes three tolerances, all of which simultaneously apply:

• Radius tolerance: maximum relative difference between a point and the radius of the first three points in the candidate arc. Defaults to 1e-6. Here PostGIS uses a hardcoded absolute difference of 1e-8. QGIS also uses an absolute difference.
• Maximum arc step size: Corresponds to the same parameter in GEOSCurveToLine. Hardcoded in PostGIS at ~45 degrees, depending on the total angle of arc. (2 edges/quadrant). Defaults in GEOS to the same.
• Maximum exterior angle difference between successive vertices. Hardcoded in PostGIS at 1e-8 radians. Much looser default in GEOS: 1e-2 radians.

Each of these tolerances is set with a separate function:

GEOSLineToCurveParams_setRadiusTolerance
GEOSLineToCurveParams_setMaxStepDegrees
GEOSLineToCurveParams_setMaxAngleDifferenceDegrees

To me, this better indicates that the three tolerances apply simultaneously, unlike the GEOSCurveToLine tolerance. But the three functions could be replaced with a GEOSLineToCurve_setTolerance(int toleranceType, double toleranceValue).

Automatic conversion

Functions that do not natively support curved types have been modified to optionally convert inputs/outputs from/to curved types. This allows a client like QGIS to delegate an operation to GEOS without having to know if the linked version of GEOS supports curved inputs for that operation.

Curve conversion is enabled at the context handle level.

Setting the curve-to-line parameters on the context (GEOSContext_setCurveToLineParams_r) will cause input curved types to be converted to linear types, if needed.

Setting line-to-curve parameters on the context (GEOSContext_setLineToCurveParams) will cause output linear types to be converted to curved types, if the inputs were themselves converted from curves.

Automatic curve conversion is not enabled on the non-reentrant API. (Should it be?)

[rouault]

I only (quickly) looked at the capi/ changes

[rouault]

Perhaps the doc could be a bit more explicit that you cannot call this function several times with different toleranceType value, hoping they would cumulate. I only figured that out by comparing with the LineToCurve API where there are different functions for the different parameters

[dbaston]

Improved in 0a0ee0a

[dbaston]

Maybe I should scrap the enum, add separate functions GEOSCurveToLineParams_setMaxAngle, and GEOSCurveToLineParams_setMaxDeviation, and pick the most restrictive tolerance during linearization ?

[rouault]

Maybe I should scrap the enum, add separate functions GEOSCurveToLineParams_setMaxAngle, and GEOSCurveToLineParams_setMaxDeviation, and pick the most restrictive tolerance during linearization ?

Yes, even more natural/obvious for users