public void CrossProduct()
{
{
var v0 = new v8 <Motion>(1, 1, 1, 2, 2, 2);
var v1 = new v8 <Motion>(-1, -2, -3, -4, -5, -6);
var r0 = Math_.Cross(v0, v1);
var r1 = Math_.CPM(v0) * v1;
Assert.True(Math_.FEql(r0, r1));
}
{
var v0 = new v8 <Force>(1, 1, 1, 2, 2, 2);
var v1 = new v8 <Force>(-1, -2, -3, -4, -5, -6);
var r0 = Math_.Cross(v0, v1);
var r1 = Math_.CPM(v0) * v1;
Assert.True(Math_.FEql(r0, r1));
}
{ // Test: vx* == -Transpose(vx)
var rng = new Random(321);
var v = v8 <IVectorSpace> .Random(-5f, +5f, rng);
var m0 = Math_.CPM(v.Cast <Motion>()); // vx
var m1 = Math_.CPM(v.Cast <Force>()); // vx*
var m2 = Math_.Transpose(m1);
var m3 = (-m2).Cast <Motion, Motion>();
Assert.True(Math_.FEql(m0, m3));
}
}
public void Basic()
{
var rng = new Random(1);
var M = m4x4.Random4x4(-5, +5, rng);
// Compare with m4x4
var m = new Matrix(4, 4);
for (int v = 0; v != 4; ++v)
{
for (int c = 0; c != 4; ++c)
{
m[v, c] = M[v][c];
}
}
Assert.True(Matrix.FEql(m, M));
Assert.True(Math_.FEql(M.w.x, m[3, 0]));
Assert.True(Math_.FEql(M.x.w, m[0, 3]));
Assert.True(Math_.FEql(M.z.z, m[2, 2]));
Assert.True(Math_.IsInvertible(M));
Assert.True(Matrix.IsInvertible(m));
var M1 = Math_.Invert(M);
var m1 = Matrix.Invert(m);
Assert.True(Matrix.FEql(m1, M1));
var M2 = Math_.Transpose(M);
var m2 = Matrix.Transpose(m);
Assert.True(Matrix.FEql(m2, M2));
}
[Test] public void Translation()
{
var m1 = new m4x4(v4.XAxis, v4.YAxis, v4.ZAxis, new v4(1.0f, 2.0f, 3.0f, 1.0f));
var m2 = m4x4.Translation(new v4(1.0f, 2.0f, 3.0f, 1.0f));
Assert.True(Math_.FEql(m1, m2));
}
[Test] public void Identity()
{
var m1 = m4x4.Identity;
var m2 = m4x4.Identity;
var m3 = m1 * m2;
Assert.True(Math_.FEql(m3, m4x4.Identity));
}
/// <summary>Compare sizes for approximate equality</summary>
public static bool FEql(Rect lhs, Rect rhs)
{
return
(Math_.FEql(lhs.X, rhs.X) &&
Math_.FEql(lhs.Y, rhs.Y) &&
Math_.FEql(lhs.Width, rhs.Width) &&
Math_.FEql(lhs.Height, rhs.Height));
}
public void TestMultiply()
{
var m1 = new m3x4(new v4(1, 2, 3, 4), new v4(1, 1, 1, 1), new v4(4, 3, 2, 1));
var m2 = new m3x4(new v4(1, 1, 1, 1), new v4(2, 2, 2, 2), new v4(-2, -2, -2, -2));
var m3 = new m3x4(new v4(6, 6, 6, 0), new v4(12, 12, 12, 0), new v4(-12, -12, -12, 0));
var r = m1 * m2;
Assert.True(Math_.FEql(r, m3));
}
[Test] public void TestTimeSpan()
{
const string expr_short = "1428d 21h 33m 9s";
const string expr_long = "1428days 21hrs 33mins 9secs";
{
var ts = TimeSpan.FromSeconds(123456789);
var s = ts.ToPrettyString();
Assert.Equal(s, expr_short);
var TS = TimeSpan_.TryParseExpr(expr_long);
Assert.Equal(TS, ts);
}
{
var ts = TimeSpan_.TryParseExpr("1d 12Hrs 1min 100secs 5msec");
var TS = new TimeSpan(1, 12, 1, 100, 5);
Assert.Equal(ts, TS);
}
{
var ts = TimeSpan_.TryParseExpr("-2mins") ?? throw new Exception("Invalid timespan expression");
var s1 = ts.ToPrettyString();
var s2 = ts.ToPrettyString(short_format: false, min_unit: TimeSpan_.ETimeUnits.Milliseconds, trailing_zeros: true);
var s3 = ts.ToPrettyString(short_format: false, min_unit: TimeSpan_.ETimeUnits.Milliseconds, trailing_zeros: false);
Assert.Equal(s1, "-2m 0s");
Assert.Equal(s2, "-2mins 0secs 0msecs");
Assert.Equal(s3, "-2mins");
}
{
var ts = TimeSpan_.TryParseExpr("0mins") ?? throw new Exception("Invalid timespan expression");
var s1 = ts.ToPrettyString();
Assert.Equal(s1, "0s");
}
{
var ts = TimeSpan_.TryParseExpr("2ms") ?? throw new Exception("Invalid timespan expression");
var s1 = ts.ToPrettyString();
var s2 = ts.ToPrettyString(min_unit: TimeSpan_.ETimeUnits.Milliseconds);
Assert.Equal(s1, "0s");
Assert.Equal(s2, "2ms");
}
{
var ts = TimeSpan_.TryParseExpr("10y 25w 7d") ?? throw new Exception("Invalid timespan expression");
var s1 = ts.ToPrettyString(trailing_zeros: false);
var s2 = ts.ToPrettyString(max_unit: TimeSpan_.ETimeUnits.Years, trailing_zeros: false);
Assert.True(Math_.FEql(ts.TotalDays, 10 * 365 + 25 * 7 + 7));
Assert.Equal(s1, "3832d");
Assert.Equal(s2, "10y 26w");
}
{
var ts = TimeSpan_.TryParseExpr("-10y 25w 7d") ?? throw new Exception("Invalid timespan expression");
var s1 = ts.ToPrettyString(trailing_zeros: false);
var s2 = ts.ToPrettyString(max_unit: TimeSpan_.ETimeUnits.Years, trailing_zeros: false);
Assert.True(Math_.FEql(ts.TotalDays, -10 * 365 + 25 * 7 + 7));
Assert.Equal(s1, "-3468d");
Assert.Equal(s2, "-9y -26w -1d");
}
}
public void DotProduct()
{
var a = new v8 <Motion>(+1, +2, +3, +4, +5, +6);
var b = new v8 <Force>(-1, -2, -3, -4, -5, -6);
var pwr0 = Math_.Dot(a, b);
var pwr1 = Math_.Dot(b, a);
Assert.True(Math_.FEql(pwr0, -91));
Assert.True(Math_.FEql(pwr1, -91));
}
[Test] public void CreateFrom3()
{
var rng = new Random(123456789);
var a2b = m4x4.Transform(v4.Random3N(0.0f, rng), rng.FloatC(0.0f, 1.0f), v4.Random3(0.0f, 10.0f, 1.0f, rng));
var b2a = Math_.Invert(a2b);
var a2a = b2a * a2b;
Assert.True(Math_.FEql(m4x4.Identity, a2a));
var b2a_fast = Math_.InvertFast(a2b);
Assert.True(Math_.FEql(b2a_fast, b2a));
}
[Test] public void CreateFrom()
{
var rnd = new Random(123456789);
var V1 = v4.Random3(0.0f, 10.0f, 1.0f, rnd);
var a2b = m4x4.Transform(v4.Random3N(0.0f, rnd), rnd.FloatC(0, (float)Math_.TauBy2), v4.Random3(0.0f, 10.0f, 1.0f, rnd));
var b2c = m4x4.Transform(v4.Random3N(0.0f, rnd), rnd.FloatC(0, (float)Math_.TauBy2), v4.Random3(0.0f, 10.0f, 1.0f, rnd));
Assert.True(Math_.IsOrthonormal(a2b));
Assert.True(Math_.IsOrthonormal(b2c));
var V2 = a2b * V1;
var V3 = b2c * V2;
var a2c = b2c * a2b;
var V4 = a2c * V1;
Assert.True(Math_.FEql(V3, V4));
}
[Test] public void CreateFrom2()
{
var m1 = m4x4.Transform(1.0f, 0.5f, 0.7f, v4.Origin);
var m2 = new m4x4(new quat(1.0f, 0.5f, 0.7f), v4.Origin);
Assert.True(Math_.IsOrthonormal(m1));
Assert.True(Math_.IsOrthonormal(m2));
Assert.True(Math_.FEql(m1, m2));
var rng = new Random(123456879);
var ang = rng.FloatC(0.0f, 1.0f);
var axis = v4.Random3N(0.0f, rng);
m1 = m4x4.Transform(axis, ang, v4.Origin);
m2 = new m4x4(new quat(axis, ang), v4.Origin);
Assert.True(Math_.IsOrthonormal(m1));
Assert.True(Math_.IsOrthonormal(m2));
Assert.True(Math_.FEql(m1, m2));
}
[Test] public void TestInversion()
{
var rng = new Random();
//{
// var m = m2x2.Random(rng, v4.Random3N(0, rng), -(float)Math_.Tau, +(float)Math_.Tau);
// var inv_m0 = m3x4.InvertFast(m);
// var inv_m1 = m3x4.Invert(m);
// Assert.True(m3x4.FEql(inv_m0, inv_m1, 0.001f));
//}
{
//m2x2.Random(rng, -5.0f, +5.0f);
var m = new m2x2(
new v2(-3.0f, +4.2f),
new v2(1.2f, -0.3f));
var inv_m = Math_.Invert(m);
var I0 = inv_m * m;
var I1 = m * inv_m;
Assert.True(Math_.FEql(I1, m2x2.Identity));
Assert.True(Math_.FEql(I0, m2x2.Identity));
}
{
var m = new m2x2(
new v2(4f, 7f),
new v2(2f, 6f));
var inv_m = Math_.Invert(m);
var det = 4f * 6f - 7f * 2f;
var INV_M = new m2x2(
new v2(6f, -7f) / det,
new v2(-2f, 4f) / det);
Assert.True(Math_.FEql(m * INV_M, m2x2.Identity));
Assert.True(Math_.FEql(inv_m, INV_M));
}
}
[Test] public void FromLinearRegression()
{
{
var pts = new v2[]
{
new v2(0, 15),
new v2(1, 13),
new v2(2, 10),
new v2(3, 7),
new v2(4, 4),
new v2(5, 1),
};
var m = Monic.FromLinearRegression(pts);
//Assert.True(Math_.FEql(m.A, 0.689393937587738));
//Assert.True(Math_.FEql(m.B, -6.10151338577271));
}
{
var pts = new v2[]
{
new v2(0, 15),
new v2(1, 13),
new v2(2, 10),
new v2(3, 7),
new v2(4, 4),
new v2(5, 1),
new v2(6, 5),
new v2(7, 8),
new v2(8, 13),
new v2(9, 19),
};
var q = Quadratic.FromLinearRegression(pts);
Assert.True(Math_.FEql((float)q.A, 0.689394f));
Assert.True(Math_.FEql((float)q.B, -6.10151672f));
Assert.True(Math_.FEql((float)q.C, 17.3090973f));
}
}
/// <summary>Show the view3D context menu</summary>
public void ShowContextMenu()
{
if (Window == null)
{
return;
}
var context_menu = new ContextMenuStrip();
context_menu.Closed += (s, a) => Refresh();
{ // View
var view_menu = context_menu.Items.Add2(new ToolStripMenuItem("View")
{
Name = CMenuItems.View
});
{ // Show focus
var opt = view_menu.DropDownItems.Add2(new ToolStripMenuItem("Show Focus")
{
Name = CMenuItems.ViewMenu.ShowFocus
});
opt.Checked = Window.FocusPointVisible;
opt.Click += (s, a) =>
{
Window.FocusPointVisible = !Window.FocusPointVisible;
Refresh();
};
}
{ // Show Origin
var opt = view_menu.DropDownItems.Add2(new ToolStripMenuItem("Show Origin")
{
Name = CMenuItems.ViewMenu.ShowOrigin
});
opt.Checked = Window.OriginPointVisible;
opt.Click += (s, a) =>
{
Window.OriginPointVisible = !Window.OriginPointVisible;
Refresh();
};
}
{ // Show coords
}
{ // Axis Views
var opt = view_menu.DropDownItems.Add2(new ToolStripComboBox("Views")
{
Name = CMenuItems.ViewMenu.Views, DropDownStyle = ComboBoxStyle.DropDownList
});
opt.Items.Add("Views");
opt.Items.Add("Axis +X");
opt.Items.Add("Axis -X");
opt.Items.Add("Axis +Y");
opt.Items.Add("Axis -Y");
opt.Items.Add("Axis +Z");
opt.Items.Add("Axis -Z");
opt.Items.Add("Axis -X,-Y,-Z");
opt.SelectedIndex = 0;
opt.SelectedIndexChanged += (s, a) =>
{
var pos = Camera.FocusPoint;
switch (opt.SelectedIndex)
{
case 1: Camera.ResetView(v4.XAxis); break;
case 2: Camera.ResetView(-v4.XAxis); break;
case 3: Camera.ResetView(v4.YAxis); break;
case 4: Camera.ResetView(-v4.YAxis); break;
case 5: Camera.ResetView(v4.ZAxis); break;
case 6: Camera.ResetView(-v4.ZAxis); break;
case 7: Camera.ResetView(-v4.XAxis - v4.YAxis - v4.ZAxis); break;
}
Camera.FocusPoint = pos;
Refresh();
};
}
{ // Object Manager UI
//var obj_mgr_ui = new ToolStripMenuItem("Object Manager");
//view_menu.DropDownItems.Add(obj_mgr_ui);
//obj_mgr_ui.Click += (s,a) => Window.ShowObjectManager(true);
}
}
{ // Navigation
var rdr_menu = context_menu.Items.Add2(new ToolStripMenuItem("Navigation")
{
Name = CMenuItems.Navigation
});
{ // Reset View
var opt = rdr_menu.DropDownItems.Add2(new ToolStripMenuItem("Reset View")
{
Name = CMenuItems.NavMenu.ResetView
});
opt.Click += (s, a) =>
{
Camera.ResetView();
Refresh();
};
}
{ // Align to
var align_menu = rdr_menu.DropDownItems.Add2(new ToolStripMenuItem("Align")
{
Name = CMenuItems.NavMenu.Align
});
{
var opt = align_menu.DropDownItems.Add2(new ToolStripComboBox("Aligns")
{
Name = CMenuItems.NavMenu.AlignMenu.Aligns, DropDownStyle = ComboBoxStyle.DropDownList
});
opt.Items.Add("None");
opt.Items.Add("X");
opt.Items.Add("Y");
opt.Items.Add("Z");
var axis = Camera.AlignAxis;
if (Math_.FEql(axis, v4.XAxis))
{
opt.SelectedIndex = 1;
}
else if (Math_.FEql(axis, v4.YAxis))
{
opt.SelectedIndex = 2;
}
else if (Math_.FEql(axis, v4.ZAxis))
{
opt.SelectedIndex = 3;
}
else
{
opt.SelectedIndex = 0;
}
opt.SelectedIndexChanged += (s, a) =>
{
switch (opt.SelectedIndex)
{
default: Camera.AlignAxis = v4.Zero; break;
case 1: Camera.AlignAxis = v4.XAxis; break;
case 2: Camera.AlignAxis = v4.YAxis; break;
case 3: Camera.AlignAxis = v4.ZAxis; break;
}
Refresh();
};
}
}
{ // Motion lock
}
{ // Orbit
//var orbit_menu = new ToolStripMenuItem("Orbit");
//rdr_menu.DropDownItems.Add(orbit_menu);
//orbit_menu.Click += delegate {};
}
}
{ // Tools
var tools_menu = context_menu.Items.Add2(new ToolStripMenuItem("Tools")
{
Name = CMenuItems.Tools
});
{ // Measure
var opt = tools_menu.DropDownItems.Add2(new ToolStripMenuItem("Measure...")
{
Name = CMenuItems.ToolsMenu.Measure
});
opt.Click += (s, a) =>
{
ShowMeasurementUI = true;
};
}
{ // Angle
var opt = tools_menu.DropDownItems.Add2(new ToolStripMenuItem("Angle...")
{
Name = CMenuItems.ToolsMenu.Angle
});
opt.Click += (s, a) =>
{
Window.ShowAngleTool = true;
};
}
}
{ // Rendering
var rdr_menu = context_menu.Items.Add2(new ToolStripMenuItem("Rendering")
{
Name = CMenuItems.Rendering
});
{ // Solid/Wireframe/Solid+Wire
var opt = rdr_menu.DropDownItems.Add2(new ToolStripComboBox {
Name = CMenuItems.RenderingMenu.FillMode, DropDownStyle = ComboBoxStyle.DropDownList
});
opt.Items.AddRange(Enum <View3d.EFillMode> .Names.Cast <object>().ToArray());
opt.SelectedIndex = (int)Window.FillMode;
opt.SelectedIndexChanged += (s, a) =>
{
Window.FillMode = (View3d.EFillMode)opt.SelectedIndex;
Refresh();
};
}
{ // Render2D
var opt = rdr_menu.DropDownItems.Add2(new ToolStripMenuItem(Window.Camera.Orthographic ? "Perspective" : "Orthographic")
{
Name = CMenuItems.RenderingMenu.Orthographic
});
opt.Click += (s, a) =>
{
var _2d = Window.Camera.Orthographic;
Window.Camera.Orthographic = !_2d;
opt.Text = _2d ? "Perspective" : "Orthographic";
Refresh();
};
}
{ // Lighting...
var opt = rdr_menu.DropDownItems.Add2(new ToolStripMenuItem("Lighting...")
{
Name = CMenuItems.RenderingMenu.Lighting
});
opt.Click += (s, a) =>
{
Window.ShowLightingDlg();
};
}
{ // Background colour
var bk_colour_menu = rdr_menu.DropDownItems.Add2(new ToolStripMenuItem("Background Colour")
{
Name = CMenuItems.RenderingMenu.Background
});
var opt = bk_colour_menu.DropDownItems.Add2(new ToolStripButton(" "));
opt.AutoToolTip = false;
opt.BackColor = Window.BackgroundColour;
opt.Click += (s, a) =>
{
var cd = new ColourUI();
if (cd.ShowDialog() == DialogResult.OK)
{
opt.BackColor = cd.Colour;
}
};
opt.BackColorChanged += (s, a) =>
{
Window.BackgroundColour = opt.BackColor;
Refresh();
};
}
}
// Allow users to add custom menu options to the context menu
// Do this last so that users have the option of removing options they don't want displayed
OnCustomiseContextMenu(new CustomContextMenuEventArgs(context_menu));
context_menu.Show(MousePosition);
}
/// <summary>Compare sizes for approximate equality</summary>
public static bool FEql(Size lhs, Size rhs)
{
return
(Math_.FEql(lhs.Width, rhs.Width) &&
Math_.FEql(lhs.Height, rhs.Height));
}
/// <summary>Compare sizes for approximate equality</summary>
public static bool FEql(Vector lhs, Vector rhs)
{
return
(Math_.FEql(lhs.X, rhs.X) &&
Math_.FEql(lhs.Y, rhs.Y));
}
/// <summary>Compare sizes for approximate equality</summary>
public static bool FEql(Point lhs, Point rhs)
{
return
(Math_.FEql(lhs.X, rhs.X) &&
Math_.FEql(lhs.Y, rhs.Y));
}