public TVector2 Copy()
{
TVector2 ret = new TVector2(_v.x, _v.y, Tag);
return ret;
}
public TVector2 this[int index]
{
get
{
switch (index)
{
case 0:
return this.a;
case 1:
return this.b;
default:
throw new System.IndexOutOfRangeException("Invalid LineSegment2D index!");
}
}
set
{
switch (index)
{
case 0:
this.a = value;
break;
case 1:
this.b = value;
break;
default:
throw new System.IndexOutOfRangeException("Invalid LineSegment2D index!");
}
}
}
public TVector2 this[int index]
{
get
{
switch (index)
{
case 0:
return this.a;
case 1:
return this.b;
case 2:
return this.c;
case 3:
return this.d;
default:
throw new System.IndexOutOfRangeException("Invalid Quad2D index!");
}
}
set
{
switch (index)
{
case 0:
this.a = value;
break;
case 1:
this.b = value;
break;
case 2:
this.c = value;
break;
case 3:
this.d = value;
break;
default:
throw new System.IndexOutOfRangeException("Invalid Quad2D index!");
}
}
}
public string Accept(TVector2 type, string bufName)
{
return($"{bufName}.ReadVector2()");
}
public DType Accept(TVector2 type, string x)
{
throw new NotSupportedException();
}
public static DType CreateVector(TVector2 type, string x)
{
var values = SplitVectorString(x);
return(new DVector2(new System.Numerics.Vector2(float.Parse(values[0]), float.Parse(values[1]))));
}
public string Accept(TVector2 type, string fieldName, string tablesName)
{
throw new NotImplementedException();
}
public Triangle3[] GetStraightSpokePlane (TVector3 origin, float zOffset, string Tag1, string Tag2)
{
System.Collections.Generic.List<Triangle3> tris = new List<Triangle3> ();
//Calc the angle to sweep...
float inctheta = 2 * Mathf.PI / ((float)_spokeCount);
float theta = 0.0f;
float adjAngle = 0.0f;
System.Collections.Generic.List<LineSegment2D> spokelines = new System.Collections.Generic.List<LineSegment2D> ();
for (int i = 0; i < (_spokeCount + 1); i++) {
adjAngle = inctheta;
TVector2 pt1;
TVector2 pt2;
if(_hubRadius !=0){
pt1 = new TVector2((_hubRadius) * Mathf.Cos(theta) + origin.Value.x, (_hubRadius) * Mathf.Sin(theta) + origin.Value.y, VERT_SpokeEdgeTop);
}else{
pt1 = new TVector2(origin.Value.x, origin.Value.y, VERT_SpokeEdgeTop);
}
pt2 = new TVector2(_ringRadius * Mathf.Cos(theta) + origin.Value.x, _ringRadius * Mathf.Sin(theta) + origin.Value.y, VERT_SpokeEdgeTop);
LineSegment2D ls = new LineSegment2D ();
ls.a = pt1;
ls.b = pt2;
spokelines.Add (ls);
theta += (adjAngle);
}
theta = 0.0f;
for (int i = 0; i < (_spokeCount); i++) {
Quad3D q3;
var q2 = CreateQuadFromLineSegment (spokelines [i], _spokeWidthInner, _spokeWidthOuter);
q3 = new Quad3D().Create(q2, origin.Value.z);
q3.Tag = Tag1;
var qtris = q3.GetTris ();
qtris[0].Tag = q3.Tag;
qtris[0].SortOrder = _triOrder;
_triOrder += 2;
qtris[1].Tag = Tag2;
qtris[1].SortOrder = _triOrder;
_triOrder += 2;
tris.AddRange (qtris);
}
return tris.ToArray ();
}
public virtual void Accept(TVector2 type, T x)
{
DoAccept(type, x);
}
public string Accept(TVector2 type)
{
return("bright.math.Vector2");
}
public bool Accept(TVector2 type, TType x, Dictionary <DefTypeBase, bool> y, HashSet <DefTypeBase> z)
{
return(true);
}
public DType Accept(TVector2 type, XElement x, DefAssembly ass)
{
return(DataUtil.CreateVector(type, x.Value));
}
public override bool Accept(TVector2 type)
{
return(true);
}
public override object ReadJson(JsonReader reader, Type objectType, object existingValue, JsonSerializer serializer)
{
TVector2 tObj = serializer.Deserialize <TVector2>(reader);
return(new Vector2(tObj.x, tObj.y));
}
public string Accept(TVector2 type)
{
return("VECTOR2");
}
public override string Accept(TVector2 type)
{
return("Vector2");
}
public string Accept(TVector2 type, string fieldName, string logType)
{
return($"{fieldName} = default;");
}
public CircleEvent(TVector2 circumcenter, TNumber radius, Node swallowedParabolaNode)
{
Circumcenter = circumcenter;
Radius = radius;
SwallowedParabolaNode = swallowedParabolaNode;
}
public string Accept(TVector2 type)
{
return($"math.Vector2");
}
public string Accept(TVector2 type, string bufName, string fieldName)
{
return($"{fieldName} = {bufName}.readVector2();");
}
public EdgeRayData(bool isOriginBounded, TVector2 origin, TVector2 direction)
{
IsOriginBounded = isOriginBounded;
Origin = origin;
Direction = direction;
}
TVector2[] BuildUVs (System.Collections.Generic.List<Triangle3> tris)
{
_ToothPerim = GetToothPermiter(tris, new string[]{TRI_SideOuterTop});
//Build Uv's
var uvs = new List<TVector2>();
//Build uvs for planes...
var tbounds = GetUVBoundaries(tris,new string[]{TRI_GearPlaneTopA1, TRI_GearPlaneTopA2, TRI_GearPlaneTopB, TRI_GearPlaneTopC, TRI_GearPlaneTopD, TRI_GearPlaneTopE}); //Get max extents for the verticies.
var tmin = tbounds.min;
var tbsz = tbounds.size;
var bbounds = GetUVBoundaries(tris,new string[]{TRI_GearPlaneBottomA1, TRI_GearPlaneBottomA2, TRI_GearPlaneBottomB, TRI_GearPlaneBottomC, TRI_GearPlaneBottomD, TRI_GearPlaneBottomE}); //Get max extents for the verticies.
var bmin = bbounds.min;
var bbsz = bbounds.size;
var hubRange = GetUVBoundaries(tris, new string[]{TRI_HubBottom, TRI_HubSideBottom, TRI_HubTop, TRI_HubSideTop});
var hubMin = hubRange.min;
var hubSz = hubRange.size;
var spokeRange = GetUVBoundaries(tris, new string[]{TRI_SolidSpokePlaneTop, TRI_SolidSpokePlaneBottom, TRI_SpokeTop1, TRI_SpokeTop2, TRI_SpokeBottom1, TRI_SpokeBottom2, TRI_SpokeSideBottom, TRI_SpokeSideTop});
var spokeMin = spokeRange.min;
var spokeSz = spokeRange.size;
//Get UV 'Buckets'
float pad = .01f; //Padding
float hs = 1.0f / (_ToothPerim);
float vs = hs;
float toph = Mathf.Max(tbsz.x, tbsz.y) * vs; //(2.0f * _outerRadius * vs); // Top Height Scaled
float bottomh = Mathf.Max(bbsz.x, bbsz.y) * vs;//(2.0f * _outerRadius * vs * _topScale); // BottomHeight Scaled
float gh = _height * vs;//_height * vs; //Gear Height Scaled
float hh = _hubHeight * vs; //Hub Height Scaled
float spokeh = spokeSz.y * vs; //(2.0f * _ringRadius * vs);
float spokew = spokeSz.x * vs;
float sidespokeh = (_height - (_spokeIndent)) * vs * 2.0f;
//float hubcaph = (2.0f * Mathf.Sqrt((_spokeWidthInner) * (_spokeWidthInner) + (_hubRadius * _hubRadius)) * vs); //???
float hubcaph = Mathf.Max(hubSz.x, hubSz.y) * vs;
Rect topbounds = new Rect(pad, 1.0f - pad - toph, toph, toph);
Rect bottombounds = new Rect(pad, topbounds.y - bottomh - pad, bottomh, bottomh);
Rect topspokebounds = new Rect(topbounds.x + topbounds.width + pad, 1.0f - pad - spokeh, spokew, spokeh);
Rect bottomspokebounds = new Rect(topspokebounds.x, topspokebounds.y - pad - spokeh, spokew, spokeh);
float perimstarty = bottombounds.y;
if (perimstarty > bottomspokebounds.y){
perimstarty = bottomspokebounds.y;
}
Rect perimbounds = new Rect(pad, perimstarty - 2.0f * pad - gh, 1.0f - 2.0f * pad, gh);
Rect ringbounds = new Rect(pad, perimbounds.y - pad - gh, 1.0f - 2.0f * pad, gh);
Rect hubbounds = new Rect(pad, ringbounds.y - pad - hh, 1.0f - 2.0f * pad, hh);
Rect tophubcapbounds = new Rect(topspokebounds.x + topspokebounds.width + pad, topspokebounds.y, hubcaph, hubcaph);
Rect bottomhubcapbounds = new Rect(tophubcapbounds.x, tophubcapbounds.y - pad - hubcaph, hubcaph, hubcaph);
Rect spokesidebounds = new Rect(pad, pad, 1.0f - 2.0f * pad, sidespokeh + pad);
float lastoutertopx = perimbounds.x;
float lastouterbottomx = perimbounds.x;
float lastinnertopx = ringbounds.x;
float lastinnerbottomx = ringbounds.x;
float lasthubbottomx = hubbounds.x;
float lasthubtopx = hubbounds.x;
float lastspokesidetopx = spokesidebounds.x;
float lastspokesidebottomx = spokesidebounds.x;
//For top plane verts, go through and calc the UV space.
foreach (Triangle3 tri in tris) {
float x = 0.0f;
float y = 0.0f;
//float xScale = (_ToothPerim);
//float yScale = xScale;
var BottomTagList = new string[] {TRI_GearPlaneBottomA1, TRI_GearPlaneBottomA2, TRI_GearPlaneBottomB, TRI_GearPlaneBottomC, TRI_GearPlaneBottomD, TRI_GearPlaneBottomE};
if(TagContains(tri.Tag, BottomTagList)){
TVector2 uvi;
Rect itembounds = bottombounds;
float widthscalex = (1.0f / bbsz.x) * itembounds.width;
float widthscaley = (1.0f / bbsz.y) * itembounds.height;
uvi = new TVector2((tri.a.Value.x - bmin.x) * widthscalex + itembounds.x, (tri.a.Value.y - bmin.y) * widthscaley + itembounds.y, tri.a.Tag);
uvs.Add(uvi);
uvi = new TVector2((tri.b.Value.x - bmin.x) * widthscalex + itembounds.x, (tri.b.Value.y - bmin.y) * widthscaley + itembounds.y, tri.b.Tag);
uvs.Add(uvi);
uvi = new TVector2((tri.c.Value.x - bmin.x) * widthscalex + itembounds.x, (tri.c.Value.y - bmin.y) * widthscaley + itembounds.y, tri.c.Tag);
uvs.Add(uvi);
}
var TopTagList = new string[] {TRI_GearPlaneTopA1, TRI_GearPlaneTopA2, TRI_GearPlaneTopB, TRI_GearPlaneTopC, TRI_GearPlaneTopD, TRI_GearPlaneTopE};
if(TagContains(tri.Tag, TopTagList)){
TVector2 uvi;
Rect itembounds = topbounds;
float widthscalex = (1.0f / tbsz.x) * itembounds.width;
float widthscaley = (1.0f / tbsz.y) * itembounds.height;
uvi = new TVector2((tri.a.Value.x - tmin.x) * widthscalex + itembounds.x, (tri.a.Value.y - tmin.y) * widthscaley + itembounds.y, tri.a.Tag);
uvs.Add(uvi);
uvi = new TVector2((tri.b.Value.x - tmin.x) * widthscalex + itembounds.x, (tri.b.Value.y - tmin.y) * widthscaley + itembounds.y, tri.b.Tag);
uvs.Add(uvi);
uvi = new TVector2((tri.c.Value.x - tmin.x) * widthscalex + itembounds.x, (tri.c.Value.y - tmin.y) * widthscaley + itembounds.y, tri.c.Tag);
uvs.Add(uvi);
}
//Spoke Layouts
var SpokeBottomTagList = new string[] {TRI_SolidSpokePlaneBottom, TRI_SpokeBottom1, TRI_SpokeBottom2};
if(TagContains(tri.Tag, SpokeBottomTagList)){
TVector2 uvi;
Rect itembounds = bottomspokebounds;
float widthscalex = (1.0f / spokeSz.x) * itembounds.width;
float widthscaley = (1.0f / spokeSz.y) * itembounds.height;
uvi = new TVector2((tri.a.Value.x - spokeMin.x) * widthscalex + itembounds.x, (tri.a.Value.y - spokeMin.y) * widthscaley + itembounds.y, tri.a.Tag);
uvs.Add(uvi);
uvi = new TVector2((tri.b.Value.x - spokeMin.x) * widthscalex + itembounds.x, (tri.b.Value.y - spokeMin.y) * widthscaley + itembounds.y, tri.b.Tag);
uvs.Add(uvi);
uvi = new TVector2((tri.c.Value.x - spokeMin.x) * widthscalex + itembounds.x, (tri.c.Value.y - spokeMin.y) * widthscaley + itembounds.y, tri.c.Tag);
uvs.Add(uvi);
}
var SpokeTopTagList = new string[] {TRI_SolidSpokePlaneTop, TRI_SpokeTop1, TRI_SpokeTop2};
if(TagContains(tri.Tag, SpokeTopTagList)){
TVector2 uvi;
Rect itembounds = topspokebounds;
float widthscalex = (1.0f / spokeSz.x) * itembounds.width;
float widthscaley = (1.0f / spokeSz.y) * itembounds.height;
uvi = new TVector2((tri.a.Value.x - spokeMin.x) * widthscalex + itembounds.x, (tri.a.Value.y - spokeMin.y) * widthscaley + itembounds.y, tri.a.Tag);
uvs.Add(uvi);
uvi = new TVector2((tri.b.Value.x - spokeMin.x) * widthscalex + itembounds.x, (tri.b.Value.y - spokeMin.y) * widthscaley + itembounds.y, tri.b.Tag);
uvs.Add(uvi);
uvi = new TVector2((tri.c.Value.x - spokeMin.x) * widthscalex + itembounds.x, (tri.c.Value.y - spokeMin.y) * widthscaley + itembounds.y, tri.c.Tag);
uvs.Add(uvi);
}
//Side Spokes...
var TopSideSpokeList = new string[] {TRI_SpokeSideTop};
if(TagContains(tri.Tag, TopSideSpokeList)){
Rect itembounds = spokesidebounds;
TVector2 uvi1;
TVector2 uvi2;
TVector2 uvi3;
float w = Vector3.Distance(tri.c.Value, tri.b.Value) * vs;
float row = Mathf.Floor((w + lastspokesidetopx) / itembounds.width);
//float rowCount = Mathf.Ceil((_spokeCount * 2.0f * w) / itembounds.width);
float h = Vector3.Distance(tri.a.Value, tri.b.Value) * vs;
float adj = itembounds.width - (Mathf.Floor(itembounds.width / w) * w);
x = w + lastspokesidetopx - itembounds.width * row + (adj * row);
y = itembounds.y + ((h) * row) + (pad * row);
uvi1 = new TVector2(x, y, tri.Tag);
y = y + h;
uvi2 = new TVector2(x, y, tri.Tag);
x = lastspokesidetopx - itembounds.width * row + (adj * row);
uvi3 = new TVector2(x, y, tri.Tag);
lastspokesidetopx +=(w);
uvs.Add(uvi1);
uvs.Add(uvi2);
uvs.Add(uvi3);
}
var BottomSideSpokeList = new string[] {TRI_SpokeSideBottom};
if(TagContains(tri.Tag, BottomSideSpokeList)){
Rect itembounds = spokesidebounds;
TVector2 uvi1;
TVector2 uvi2;
TVector2 uvi3;
float w = Vector3.Distance(tri.a.Value, tri.c.Value) * vs;
float row = Mathf.Floor((w + lastspokesidebottomx) / itembounds.width);
//float rowCount = Mathf.Ceil((_spokeCount * 2.0f * w) / itembounds.width);
float h = Vector3.Distance(tri.b.Value, tri.c.Value) * vs;
float adj = itembounds.width - (Mathf.Floor(itembounds.width / w) * w);
x = w + lastspokesidebottomx - itembounds.width * row + (adj * row);
y = itembounds.y + ((h) * row) + (pad * row);
uvi1 = new TVector2(x, y, tri.Tag);
x = lastspokesidebottomx - itembounds.width * row + (adj * row);
uvi2 = new TVector2(x, y, tri.Tag);
y = y + h;
uvi3 = new TVector2(x, y, tri.Tag);
lastspokesidebottomx +=(w);
uvs.Add(uvi1);
uvs.Add(uvi3);
uvs.Add(uvi2);
}
//Hub Cap Layouts
var HubCapBottomTagList = new string[] {TRI_HubBottom};
if(TagContains(tri.Tag, HubCapBottomTagList)){
TVector2 uvi;
Rect itembounds = bottomhubcapbounds;
float widthscalex = (1.0f / hubSz.x) * itembounds.width;
float widthscaley = (1.0f / hubSz.y) * itembounds.height;
uvi = new TVector2((tri.a.Value.x - hubMin.x) * widthscalex + itembounds.x, (tri.a.Value.y - hubMin.y) * widthscaley + itembounds.y, tri.a.Tag);
uvs.Add(uvi);
uvi = new TVector2((tri.b.Value.x - hubMin.x) * widthscalex + itembounds.x, (tri.b.Value.y - hubMin.y) * widthscaley + itembounds.y, tri.b.Tag);
uvs.Add(uvi);
uvi = new TVector2((tri.c.Value.x - hubMin.x) * widthscalex + itembounds.x, (tri.c.Value.y - hubMin.y) * widthscaley + itembounds.y, tri.c.Tag);
uvs.Add(uvi);
}
var HubCapTopTagList = new string[] {TRI_HubTop};
if(TagContains(tri.Tag, HubCapTopTagList)){
TVector2 uvi;
Rect itembounds = tophubcapbounds;
float widthscalex = (1.0f / hubSz.x) * itembounds.width;
float widthscaley = (1.0f / hubSz.y) * itembounds.height;
uvi = new TVector2((tri.a.Value.x - hubMin.x) * widthscalex + itembounds.x, (tri.a.Value.y - hubMin.y) * widthscaley + itembounds.y, tri.a.Tag);
uvs.Add(uvi);
uvi = new TVector2((tri.b.Value.x - hubMin.x) * widthscalex + itembounds.x, (tri.b.Value.y - hubMin.y) * widthscaley + itembounds.y, tri.b.Tag);
uvs.Add(uvi);
uvi = new TVector2((tri.c.Value.x - hubMin.x) * widthscalex + itembounds.x, (tri.c.Value.y - hubMin.y) * widthscaley + itembounds.y, tri.c.Tag);
uvs.Add(uvi);
}
//Tooth Perim 1st Half
var OuterListTop = new string[] {TRI_SideOuterTop};
if(TagContains(tri.Tag, OuterListTop)){
TVector2 uvi1;
TVector2 uvi2;
TVector2 uvi3;
Rect itembounds = perimbounds;
float w = Vector3.Distance(tri.c.Value, tri.b.Value) * vs * itembounds.width; /// xScale * _topScale;
//float h = itembounds.height; // _height / yScale;
x = w + lastoutertopx;
y = itembounds.y;
uvi1 = new TVector2(x, y, tri.Tag);
x = lastoutertopx;
uvi2 = new TVector2(x, y, tri.Tag);
y = itembounds.y + itembounds.height;
uvi3 = new TVector2(x, y, tri.Tag);
lastoutertopx +=w;
uvs.Add(uvi3);
uvs.Add(uvi2);
uvs.Add(uvi1);
}
//Tooth Perim 2nd Half
var OuterListBottom = new string[] {TRI_SideOuterBottom};
if(TagContains(tri.Tag, OuterListBottom)){
TVector2 uvi1;
TVector2 uvi2;
TVector2 uvi3;
Rect itembounds = perimbounds;
float w = Vector3.Distance(tri.a.Value, tri.c.Value) * vs * itembounds.width *_topScale; /// xScale * _topScale;
//float h = itembounds.height; // _height / yScale;
x = w + lastouterbottomx;
y = itembounds.y;
uvi1 = new TVector2(x, y, tri.Tag);
y = itembounds.y + itembounds.height;
uvi2 = new TVector2(x, y, tri.Tag);
x = lastouterbottomx;
uvi3 = new TVector2(x, y, tri.Tag);
lastouterbottomx +=w;
uvs.Add(uvi3);
uvs.Add(uvi1);
uvs.Add(uvi2);
}
var InnerListTop = new string[] {TRI_SideInnerTop};
if(TagContains(tri.Tag, InnerListTop)){
TVector2 uvi1;
TVector2 uvi2;
TVector2 uvi3;
Rect itembounds = ringbounds;
float w = Vector3.Distance(tri.b.Value, tri.c.Value) * vs * itembounds.width;
//float h = itembounds.height;
x = w + lastinnertopx;
y = itembounds.y;
uvi1 = new TVector2(x, y, tri.Tag);
y = itembounds.y + itembounds.height;
uvi2 = new TVector2(x, y, tri.Tag);
x = lastinnertopx;
uvi3 = new TVector2(x, y, tri.Tag);
lastinnertopx +=w;
uvs.Add(uvi1);
uvs.Add(uvi2);
uvs.Add(uvi3);
}
var InnerListBottom = new string[] {TRI_SideInnerBottom};
if(TagContains(tri.Tag, InnerListBottom)){
TVector2 uvi1;
TVector2 uvi2;
TVector2 uvi3;
Rect itembounds = ringbounds;
float w = Vector3.Distance(tri.a.Value, tri.c.Value) * vs * itembounds.width;
//float h = _height / yScale;
x = lastinnerbottomx;
y = itembounds.y;
uvi1 = new TVector2(x, y, tri.Tag);
x = w + lastinnerbottomx;
uvi2 = new TVector2(x, y, tri.Tag);
y = itembounds.y + itembounds.height;
x = lastinnerbottomx;
uvi3 = new TVector2(x, y, tri.Tag);
lastinnerbottomx +=w;
uvs.Add(uvi2);
uvs.Add(uvi3);
uvs.Add(uvi1);
}
var HubListTop = new string[] {TRI_HubSideTop};
if(TagContains(tri.Tag, HubListTop)){
TVector2 uvi1;
TVector2 uvi2;
TVector2 uvi3;
Rect itembounds = hubbounds;
float w = Vector3.Distance(tri.c.Value, tri.b.Value) * vs * itembounds.width;
//float h = itembounds.height;
x = w + lasthubtopx;
y = itembounds.y;
uvi1 = new TVector2(x, y, tri.Tag);
x = lasthubtopx;
uvi2 = new TVector2(x, y, tri.Tag);
y = itembounds.y + itembounds.height;
uvi3 = new TVector2(x, y, tri.Tag);
lasthubtopx +=w;
uvs.Add(uvi3);
uvs.Add(uvi2);
uvs.Add(uvi1);
}
var HubListBottom = new string[] {TRI_HubSideBottom};
if(TagContains(tri.Tag, HubListBottom)){
TVector2 uvi1;
TVector2 uvi2;
TVector2 uvi3;
Rect itembounds = hubbounds;
float w = Vector3.Distance(tri.a.Value, tri.c.Value) * vs * itembounds.width;
//float h = _hubHeight / yScale;
x = w + lasthubbottomx;
y = itembounds.y;
uvi1 = new TVector2(x, y, tri.Tag);
y = itembounds.y + itembounds.height;
uvi2 = new TVector2(x, y, tri.Tag);
x = lasthubbottomx;
uvi3 = new TVector2(x, y, tri.Tag);
lasthubbottomx +=w;
uvs.Add(uvi3);
uvs.Add(uvi1);
uvs.Add(uvi2);
}
}
return uvs.ToArray();
}
public ParabolaData(TVector2 focus)
{
Focus = focus;
}
public ResizeWindowEvent(uint width, uint height) : base(GetStaticType())
{
this.size = new TVector2 <uint>(width, height);
}
public static TVector2 ComputeRayParabolaIntersection(
TVector2 rayOrigin, TVector2 rayDirection,
TVector2 parabolaFocus, TNumber directrixY)
{
if (ApproximatelyEqual(0, rayDirection.X))
{
var x = rayOrigin.X;
TNumber sa, sb, sc;
ComputeParabolaStandardForm(parabolaFocus, directrixY, out sa, out sb, out sc);
return(new Vector2(x, sa * x * x + sb * x + sc));
}
if (MathUtil.ApproximatelyEqual(directrixY, parabolaFocus.Y))
{
directrixY += 0.2f;
}
// Given an intersecting ray R and parabola P, find the first point of intersection.
//
// Let ro be the ray origin point (rox, roy)
// rd be the ray direction vector (rdx, rdy)
// pf be the parabola focus point (pfx, pfy)
// dy be the directrix y-coordinate
//
// Let t be the ray parameterization variable in [0, inf)
// s be the solution point (sx, sy), s = ro + rd * t
//
// By definition of parabola:
// dy - sy = |s - f|
// (dy - sy)^2 = |s - f|^2
//
// Expand (dy - sy)^2:
// (dy - sy)^2
// (dy - (roy + rdy * t))^2
// ((dy - roy) - rdy * t)^2
// (dy - roy)^2 - 2 (dy - roy) (rdy * t) + (rdy * t)^2
// (dy - roy)^2 - 2 (dy - roy) (rdy) t + (rdy^2) t^2
//
// Expand |s - f|^2:
// (sx - fx)^2 + (sy - fy)^2
// ((rox + rdx * t) - fx)^2 + ((roy + rdy * t) - fy)^2
//
// Expand ((rox + rdx * t) - fx)^2:
// ((rdx * t) + (rox - fx))^2
// (rdx * t)^2 + 2 (rdx * t) (rox - fx) + (rox - fx)^2
// (rdx^2) t^2 + t (2 rdx (rox - fx)) + (rox - fx)^2
//
// Expand ((roy + rdy * t) - fy)^2: (likewise)
// (rdy^2) t^2 + t (2 rdy (roy - fy)) + (roy - fy)^2
//
// (rdx^2) t^2 + t (2 rdx (rox - fx)) + (rox - fx)^2 + (rdy^2) t^2 + t (2 rdy (roy - fy)) + (roy - fy)^2
// (rdx^2 + rdy^2) t^2 + t (2 rdx (rox - fx) + 2 rdy (roy - fy)) + (rox - fx)^2 + (roy - fy)^2
//
// Back to: dy - sy = |s - f|
// (dy - sy)^2 = |s - f|^2
//
// (dy - roy)^2 - 2 (dy - roy) (rdy) t + (rdy^2) t^2 =
// (rdx^2 + rdy^2) t^2 + t (2 rdx (rox - fx) + 2 rdy (roy - fy)) + (rox - fx)^2 + (roy - fy)^2
//
// 0 = t^2 (rdx^2 + rdy^2 - rdy^2) +
// t (2 rdx (rox - fx) + 2 rdy (roy - fy) + 2 (dy - roy) (rdy)) +
// 1 ((rox - fx)^2 + (roy - fy)^2 - (dy - roy)^2)
//
// 0 = t^2 (rdx^2) +
// t (2 rdx rox - 2 rdx fx + 2 rdy roy - 2 rdy fy + 2 rdy dy - 2 rdy roy) +
// 1 (rox^2 - 2 rox fx + fx^2 + roy^2 - 2 roy fy + fy^2 - dy^2 + 2 dy roy - roy^2)
//
// 0 = t^2 (rdx^2) +
// t (2 rdx rox - 2 rdx fx - 2 rdy fy + 2 rdy dy) +
// 1 (rox^2 - 2 rox fx + fx^2 - 2 roy fy + fy^2 - dy^2 + 2 dy roy)
var roxMinusFx = rayOrigin.X - parabolaFocus.X;
var royMinusFy = rayOrigin.Y - parabolaFocus.Y;
var dyMinusRoy = directrixY - rayOrigin.Y;
var a = rayDirection.X * rayDirection.X;
var b = 2 * (rayDirection.X * roxMinusFx
- rayDirection.Y * (parabolaFocus.Y - directrixY));
var c = roxMinusFx * roxMinusFx + royMinusFy * royMinusFy - dyMinusRoy * dyMinusRoy;
TNumber pickedT = default(TNumber);
if (!MathUtil.ApproximatelyEqual(0, a))
{
var centerT = -b / (2 * a);
var offsetT = (TNumber)Math.Sqrt(b * b - 4 * a * c) / (2 * a);
var lowerT = centerT - offsetT;
var upperT = centerT + offsetT;
pickedT = lowerT >= 0 ? lowerT : upperT;
}
if (TNumber.IsNaN(pickedT))
{
// Debugger.Break();
pickedT = 0;
}
return(rayOrigin + pickedT * rayDirection);
}
public DType Accept(TVector2 type, IEnumerable <ExcelStream> x, bool y, DefAssembly ass)
{
throw new NotImplementedException();
}
public static TVector2 ComputeRayPointAtY(TVector2 rayOrigin, TVector2 rayDirection, TNumber y)
{
var dy = y - rayOrigin.Y;
return(rayOrigin + (rayDirection * dy) / rayDirection.Y);
}
public string Accept(TVector2 type, string jsonVarName, string fieldName)
{
return($"{fieldName} = Vector2.fromJson({jsonVarName});");
}
public static TVector2 ComputeParabolaPointGivenX(TNumber rx, TNumber directrixY, TVector2 focus)
{
// Let result be a point r (rx, ry) located between the focus's y and directrix y.
// directrixY - ry = sqrt((rx - focusX)^2 + (ry - focusY)^2)
// (directrixY - ry)^2 = (rx - focusX)^2 + (ry - focusY)^2
// directrixY^2 - 2 directrixY ry + ry^2 = rx^2 - 2 rx focusX + focusX^2 + ry^2 - 2 ry focusY + focusY^2
// -2 directrixY ry + ry^2 = rx^2 - 2 rx focusX + focusX^2 + ry^2 - 2 ry focusY + focusY^2 - directrixY^2
// -2 directrixY ry + ry^2 - ry^2 + 2 ry focusY = rx^2 - 2 rx focusX + focusX^2 + focusY^2 - directrixY^2
// -2 directrixY ry + 2 ry focusY = rx^2 - 2 rx focusX + focusX^2 + focusY^2 - directrixY^2
// ry (-2 directrixY + 2 focusY) = rx^2 - 2 rx focusX + focusX^2 + focusY^2 - directrixY^2
// ry = (rx^2 - 2 rx focusX + focusX^2 + focusY^2 - directrixY^2) / (-2 directrixY + 2 focusY)
var numerator = rx * rx - 2 * rx * focus.X + focus.X * focus.X + focus.Y * focus.Y - directrixY * directrixY;
var denominator = -2 * directrixY + 2 * focus.Y;
var ry = numerator / denominator;
return(new TVector2(rx, ry));
}
public virtual TR Accept(TVector2 type)
{
return DoAccept(type);
}
void ProcessCircleEvent(FortunesAlgorithmState state, CircleEvent e)
{
var sweepY = e.Y;
var swallowedParabolaNode = e.SwallowedParabolaNode;
if (swallowedParabolaNode.Parent == null)
{
return;
}
Node leftAncestor, rightAncestor;
swallowedParabolaNode.FindDirectionalAncestors(out leftAncestor, out rightAncestor);
var leftAncestorEdgeRayData = (EdgeRayData)leftAncestor.Data;
var rightAncestorEdgeRayData = (EdgeRayData)rightAncestor.Data;
state.VoronoiEdges.Add(new VoronoiEdge(
leftAncestorEdgeRayData.Origin, leftAncestorEdgeRayData.IsOriginBounded, e.Circumcenter, true));
state.VoronoiEdges.Add(new VoronoiEdge(
rightAncestorEdgeRayData.Origin, leftAncestorEdgeRayData.IsOriginBounded, e.Circumcenter, true));
var leftParabolaNode = leftAncestor.Left.GetRightmost();
var leftParabolaFocus = ((ParabolaData)leftParabolaNode.Data).Focus;
var rightParabolaNode = rightAncestor.Right.GetLeftmost();
var rightParabolaFocus = ((ParabolaData)rightParabolaNode.Data).Focus;
state.DelanayEdges.Add(new VoronoiEdge(leftParabolaFocus, true, rightParabolaFocus, true));
// One ancestor will become the edge shared by the left/right parabolas,
// the other will be deleted. It's guranteed our parent is one of these
// ancestors and that the other ancestor is above it (that is, it has a
// parent) so opt to delete our parent.
var nodeParent = swallowedParabolaNode.Parent;
var nodeSibling = nodeParent.Left == swallowedParabolaNode ? nodeParent.Right : nodeParent.Left;
NodeOperations.ReplaceNode(nodeParent, nodeSibling, ref state.Root);
nodeParent.Left = nodeParent.Right = null;
var olderAncestor = nodeParent == leftAncestor ? rightAncestor : leftAncestor;
var leftFocusRightFocus = rightParabolaFocus - leftParabolaFocus; // x is positive
var edgeDirection = new TVector2(-leftFocusRightFocus.Y, leftFocusRightFocus.X);
var leftRightFocusCenter = new TVector2(
MathUtil.Average(leftParabolaFocus.X, rightParabolaFocus.X),
MathUtil.Average(leftParabolaFocus.Y, rightParabolaFocus.Y));
var dy = sweepY - leftRightFocusCenter.Y;
var edgeStart = e.Circumcenter;
olderAncestor.Data = new EdgeRayData(true, edgeStart, edgeDirection);
// add new potential circle events
Node leftLeftLeaf;
if (leftParabolaNode.TryGetLeftLeaf(out leftLeftLeaf))
{
HandleAddCircleEvent(state, leftLeftLeaf, leftParabolaNode, rightParabolaNode, sweepY);
}
Node rightRightLeaf;
if (rightParabolaNode.TryGetRightLeaf(out rightRightLeaf))
{
HandleAddCircleEvent(state, leftParabolaNode, rightParabolaNode, rightRightLeaf, sweepY);
}
}
private void DrawPointX(Graphics g, TVector2 point, int dims, Pen pen = null)
{
g.DrawLine(pen ?? Pens.Black, point.X - dims, point.Y - dims, point.X + dims, point.Y + dims);
g.DrawLine(pen ?? Pens.Black, point.X + dims, point.Y - dims, point.X - dims, point.Y + dims);
}
public SiteEvent(TVector2 point)
{
Point = point;
}
public string Accept(TVector2 type, string bufName, string fieldName)
{
return($"{bufName}.WriteVector2({fieldName});");
}
public void Accept(TVector2 type, Dictionary <string, DefTypeBase> x)
{
}
