Scripts/verlet-chains.ps1
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# Unique Concept: Verlet physics rope simulation with hanging chains and wave propagation. # Shows connected particles with constraint satisfaction creating realistic swaying motion. $ErrorActionPreference = 'Stop' $esc = [char]27 $reset = "$esc[0m" function Convert-HsvToRgb { param([double]$Hue, [double]$Saturation, [double]$Value) $h = ($Hue % 1) * 6 $sector = [math]::Floor($h) $fraction = $h - $sector $p = $Value * (1 - $Saturation) $q = $Value * (1 - $fraction * $Saturation) $t = $Value * (1 - (1 - $fraction) * $Saturation) switch ($sector) { 0 { $r = $Value; $g = $t; $b = $p } 1 { $r = $q; $g = $Value; $b = $p } 2 { $r = $p; $g = $Value; $b = $t } 3 { $r = $p; $g = $q; $b = $Value } 4 { $r = $t; $g = $p; $b = $Value } default { $r = $Value; $g = $p; $b = $q } } return @([int][math]::Round($r * 255), [int][math]::Round($g * 255), [int][math]::Round($b * 255)) } $width = 100 $height = 26 # Create multiple ropes $ropes = @() for ($ropeId = 0; $ropeId -lt 5; $ropeId++) { $anchorX = 15 + $ropeId * 18 $particles = for ($i = 0; $i -lt 20; $i++) { @{ X = $anchorX + [math]::Sin($i * 0.5 + $ropeId) * 2 Y = $i * 1.2 OldX = $anchorX + [math]::Sin($i * 0.5 + $ropeId) * 2 OldY = $i * 1.2 Fixed = ($i -eq 0) } } $ropes += , @{ Particles = $particles; Hue = $ropeId / 5.0 } } # Simulate Verlet integration $iterations = 8 for ($sim = 0; $sim -lt $iterations; $sim++) { foreach ($rope in $ropes) { # Update positions foreach ($p in $rope.Particles) { if ($p.Fixed) { continue } $vx = $p.X - $p.OldX $vy = $p.Y - $p.OldY $p.OldX = $p.X $p.OldY = $p.Y $p.X += $vx * 0.98 + [math]::Sin($sim * 0.3) * 0.15 $p.Y += $vy * 0.98 + 0.08 # Gravity } # Constraint satisfaction for ($iter = 0; $iter -lt 3; $iter++) { for ($i = 0; $i -lt ($rope.Particles.Count - 1); $i++) { $p1 = $rope.Particles[$i] $p2 = $rope.Particles[$i + 1] $dx = $p2.X - $p1.X $dy = $p2.Y - $p1.Y $dist = [math]::Sqrt($dx * $dx + $dy * $dy) $targetDist = 1.2 if ($dist -gt 0.01) { $diff = ($targetDist - $dist) / $dist * 0.5 $offsetX = $dx * $diff $offsetY = $dy * $diff if (-not $p1.Fixed) { $p1.X -= $offsetX $p1.Y -= $offsetY } if (-not $p2.Fixed) { $p2.X += $offsetX $p2.Y += $offsetY } } } } } } # Render $grid = @{} foreach ($rope in $ropes) { for ($i = 0; $i -lt ($rope.Particles.Count - 1); $i++) { $p1 = $rope.Particles[$i] $p2 = $rope.Particles[$i + 1] # Draw line between particles $steps = 5 for ($s = 0; $s -le $steps; $s++) { $t = $s / [double]$steps $x = [int]($p1.X + ($p2.X - $p1.X) * $t) $y = [int]($p1.Y + ($p2.Y - $p1.Y) * $t) if ($x -ge 0 -and $x -lt $width -and $y -ge 0 -and $y -lt $height) { $key = "$x,$y" $grid[$key] = @{ Hue = $rope.Hue Index = $i } } } } } for ($row = 0; $row -lt $height; $row++) { $sb = [System.Text.StringBuilder]::new() for ($col = 0; $col -lt $width; $col++) { $key = "$col,$row" if ($grid.ContainsKey($key)) { $cell = $grid[$key] $hue = ($cell.Hue + $cell.Index * 0.03) % 1 $saturation = 0.7 $value = 0.9 - $cell.Index * 0.02 $rgb = Convert-HsvToRgb -Hue $hue -Saturation $saturation -Value $value $symbol = '●' $null = $sb.Append("$esc[38;2;$($rgb[0]);$($rgb[1]);$($rgb[2])m$symbol") } else { $null = $sb.Append("$esc[38;2;8;8;12m ") } } Write-Host ($sb.ToString() + $reset) } Write-Host $reset |