commit 89b935767c6b5674726dc80800c71156d0b9277e Author: Leszek Koltunski Date: Mon Dec 17 15:45:22 2018 +0000 Add support for MeshSphere (add ability to display it in the 'Effects3D' and 'Inflate' apps). Still a bit buggy! diff --git a/src/main/java/org/distorted/library/mesh/MeshSphere.java b/src/main/java/org/distorted/library/mesh/MeshSphere.java new file mode 100644 index 0000000..262a5d9 --- /dev/null +++ b/src/main/java/org/distorted/library/mesh/MeshSphere.java @@ -0,0 +1,255 @@ +/////////////////////////////////////////////////////////////////////////////////////////////////// +// Copyright 2018 Leszek Koltunski // +// // +// This file is part of Distorted. // +// // +// Distorted is free software: you can redistribute it and/or modify // +// it under the terms of the GNU General Public License as published by // +// the Free Software Foundation, either version 2 of the License, or // +// (at your option) any later version. // +// // +// Distorted is distributed in the hope that it will be useful, // +// but WITHOUT ANY WARRANTY; without even the implied warranty of // +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // +// GNU General Public License for more details. // +// // +// You should have received a copy of the GNU General Public License // +// along with Distorted. If not, see . // +/////////////////////////////////////////////////////////////////////////////////////////////////// + +package org.distorted.library.mesh; + +/////////////////////////////////////////////////////////////////////////////////////////////////// +/** + * Create a Mesh which approximates a sphere. + *

+ * Do so by dividing each of the 20 faces of the regular icosahedron into smaller triangles and inflating + * those to lay on the surface of the sphere. + */ +public class MeshSphere extends MeshBase + { + private static final int NUMFACES = 20; + private static final double sqrt2 = Math.sqrt(2.0); + private static final double P = Math.PI; + private static final double A = 0.463647609; // arctan(0.5), +-latitude of the 10 'middle' vertices + // https://en.wikipedia.org/wiki/Regular_icosahedron + + // An array of 20 entries, each describing a single face of the regular icosahedron in an (admittedly) + // weird fashion. + // Each face of a regular icosahedron is a equilateral triangle, with 2 vertices on the same latitude. + // Single row is (longitude of V1, longitude of V2, (common) latitude of V1 and V2, latitude of V3) + // longitude of V3 is simply midpoint of V1 and V2 so we don't have to specify it here. + + private static final double FACES[][] = { + { 0.0 , 0.4*P, A, 0.5*P }, + { 0.4*P, 0.8*P, A, 0.5*P }, + { 0.8*P, 1.2*P, A, 0.5*P }, // 5 'top' faces with + { 1.2*P, 1.6*P, A, 0.5*P }, // the North Pole + { 1.6*P, 2.0*P, A, 0.5*P }, + + { 0.0 , 0.4*P, A, -A }, + { 0.4*P, 0.8*P, A, -A }, + { 0.8*P, 1.2*P, A, -A }, // 5 faces mostly above + { 1.2*P, 1.6*P, A, -A }, // the equator + { 1.6*P, 2.0*P, A, -A }, + + { 0.2 , 0.6*P, -A, A }, + { 0.6*P, 1.0*P, -A, A }, + { 1.0*P, 1.4*P, -A, A }, // 5 faces mostly below + { 1.4*P, 1.8*P, -A, A }, // the equator + { 1.8*P, 0.2*P, -A, A }, + + { 0.2 , 0.6*P, -A,-0.5*P }, + { 0.6*P, 1.0*P, -A,-0.5*P }, + { 1.0*P, 1.4*P, -A,-0.5*P }, // 5 'bottom' faces with + { 1.4*P, 1.8*P, -A,-0.5*P }, // the South Pole + { 1.8*P, 0.2*P, -A,-0.5*P } + }; + private int currentVert; + private int numVertices; + +/////////////////////////////////////////////////////////////////////////////////////////////////// +// Each of the 20 faces of the icosahedron requires (level*level + 4*level) vertices for the face +// itself and a join to the next face (which requires 2 vertices). We don't need the join in case +// of the last, 20th face, thus the -2. +// (level*level +4*level) because there are level*level little triangles, each requiring new vertex, +// plus 2 extra vertices to start off a row and 2 to move to the next row (or the next face in case +// of the last row) and there are 'level' rows. + + private void computeNumberOfVertices(int level) + { + numVertices = 20*level*(level+4) -2; + currentVert = 0; + } + +/////////////////////////////////////////////////////////////////////////////////////////////////// +// (longitude,latitude) - spherical coordinates of a point on a unit sphere. +// Cartesian (0,0,1) - i.e. the point of the sphere closest to the camera - is spherical (0,0). + + private void addVertex( double longitude, double latitude, float[] attribs) + { + double sinLON = Math.sin(longitude); + double cosLON = Math.cos(longitude); + double sinLAT = Math.sin(latitude); + double cosLAT = Math.cos(latitude); + + float x = (float)(cosLAT*sinLON / sqrt2); + float y = (float)(sinLAT / sqrt2); + float z = (float)(cosLAT*cosLON / sqrt2); + + attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB ] = x; // + attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB+1] = y; // + attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB+2] = z; // + // In case of this Mesh so it happens that + attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB ] = x; // the vertex coords, normal vector, and + attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB+1] = y; // inflate vector have identical (x,y,z). + attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB+2] = z; // + // TODO: think about some more efficient + attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB ] = x; // representation. + attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB+1] = y; // + attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB+2] = z; // + + attribs[VERT_ATTRIBS*currentVert + TEX_ATTRIB ] = (float)longitude; + attribs[VERT_ATTRIBS*currentVert + TEX_ATTRIB+1] = (float)latitude; + + currentVert++; + } + + +/////////////////////////////////////////////////////////////////////////////////////////////////// + + private void repeatLast(float[] attribs) + { + if( currentVert>0 ) + { + attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB ] = attribs[VERT_ATTRIBS*(currentVert-1) + POS_ATTRIB ]; + attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-1) + POS_ATTRIB+1]; + attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB+2] = attribs[VERT_ATTRIBS*(currentVert-1) + POS_ATTRIB+2]; + + attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB ] = attribs[VERT_ATTRIBS*(currentVert-1) + NOR_ATTRIB ]; + attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-1) + NOR_ATTRIB+1]; + attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB+2] = attribs[VERT_ATTRIBS*(currentVert-1) + NOR_ATTRIB+2]; + + attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB ] = attribs[VERT_ATTRIBS*(currentVert-1) + INF_ATTRIB ]; + attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-1) + INF_ATTRIB+1]; + attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB+2] = attribs[VERT_ATTRIBS*(currentVert-1) + INF_ATTRIB+2]; + + attribs[VERT_ATTRIBS*currentVert + TEX_ATTRIB ] = attribs[VERT_ATTRIBS*(currentVert-1) + TEX_ATTRIB ]; + attribs[VERT_ATTRIBS*currentVert + TEX_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-1) + TEX_ATTRIB+1]; + + currentVert++; + } + } + +/////////////////////////////////////////////////////////////////////////////////////////////////// +// Supposed to return the latitude of the point between two points on the sphere with latitudes +// lat1 and lat2, so if for example quot=0.2, then it will return the latitude of something 20% +// along the way from lat1 to lat2. +// +// This is approximation only - in general it is of course not true that the midpoint of two points +// on a unit sphere with spherical coords (A1,B1) and (A2,B2) is ( (A1+A2)/2, (B1+B2)/2 ) - take +// (0,0) and (PI, epsilon) as a counterexample. +// +// Here however, the latitudes we are interested at are the latitudes of the vertices of a regular +// icosahedron - i.e. +=A and +=PI/2, whose longitudes are close, and we don't really care if the +// split into smaller triangles is exact. +// +// quot better be between 0.0 and 1.0. +// this is 'directed' i.e. from lat1 to lat2. + + private double midLatitude(double lat1, double lat2, double quot) + { + return lat1*(1.0-quot)+lat2*quot; + } + +/////////////////////////////////////////////////////////////////////////////////////////////////// +// Same in case of longitude. This is for our needs exact, because we are ever only calling this with +// two longitudes of two vertices with the same latitude. Additional problem: things can wrap around +// the circle. +// this is 'undirected' i.e. we don't assume from lon1 to lon2 - just along the smaller arc joining +// lon1 to lon2. + + private double midLongitude(double lon1, double lon2, double quot) + { + double min, max; + + if( lon1P ) { diff=2*P-diff; min=max; } + + double ret = min+quot*diff; + if( ret>=2*P ) ret-=2*P; + + return ret; + } + +/////////////////////////////////////////////////////////////////////////////////////////////////// +// linear map (column,row, level): +// +// ( 0, 0, level) -> (lonV1,latV12) +// ( 0, level-1, level) -> (lonV3,latV3 ) +// (level-1, 0, level) -> (lonV2,latV12) + + private void newVertex(float[] attribs, int column, int row, int level, + double lonV1, double lonV2, double latV12, double latV3) + { + double quotX = (double)column/(level-1); + double quotY = (double)row /(level-1); + + double lonPoint = midLongitude(lonV1,lonV2, (quotX+0.5*quotY) ); + double latPoint = midLatitude(latV12,latV3, quotY); + + addVertex(lonPoint,latPoint,attribs); + } + +/////////////////////////////////////////////////////////////////////////////////////////////////// + + private void buildFace(float[] attribs, int level, int face, double lonV1, double lonV2, double latV12, double latV3) + { + for(int row=0; row + * When level=1, it outputs the 12 vertices of a regular icosahedron. + * When level=N, it divides each of the 20 icosaherdon's triangular faces into N^2 smaller triangles + * (by dividing each side into N equal segments) and 'inflates' the internal vertices so that they + * touch the sphere. + * + * @param level Specifies the approximation level. Valid values: level ≥ 1 + */ + public MeshSphere(int level) + { + super(1.0f); + + computeNumberOfVertices(level); + float[] attribs= new float[VERT_ATTRIBS*numVertices]; + + for(int face=0; face