// Copyright 2023 Google Inc. All rights reserved. // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. package s2 const ( // maxEdgeDeviationRatio is set so that MaxEdgeDeviation will be large enough // compared to snapRadius such that edge splitting is rare. // // Using spherical trigonometry, if the endpoints of an edge of length L // move by at most a distance R, the center of the edge moves by at most // asin(sin(R) / cos(L / 2)). Thus the (MaxEdgeDeviation / SnapRadius) // ratio increases with both the snap radius R and the edge length L. // // We arbitrarily limit the edge deviation to be at most 10% more than the // snap radius. With the maximum allowed snap radius of 70 degrees, this // means that edges up to 30.6 degrees long are never split. For smaller // snap radii, edges up to 49 degrees long are never split. (Edges of any // length are not split unless their endpoints move far enough so that the // actual edge deviation exceeds the limit; in practice, splitting is rare // even with long edges.) Note that it is always possible to split edges // when MaxEdgeDeviation is exceeded. maxEdgeDeviationRatio = 1.1 )