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I am trying to plot a function $ {\bf x}(t) = a(t)\hat{v} + {\bf b}(t) $$ {\bf x}(t) = r(t)\hat{v} + {\bf b}(t) $, with unit vector $ \hat{v} $ and vector $ {\bf b}(t) $ given in spherical coordinates. For simplicity, assume that $ \hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta) $, and $ {\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)] $, where $ a $ and $ b $ are constants. This is easy to plot, however, I want the angles $ \theta $ and $ \phi $ to satisfy an implicit equation, say, $ \cos\theta + a(\phi + b t)^2 + c = 0 $.

I am trying to plot a function $ {\bf x}(t) = a(t)\hat{v} + {\bf b}(t) $, with unit vector $ \hat{v} $ and vector $ {\bf b}(t) $ given in spherical coordinates. For simplicity, assume that $ \hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta) $, and $ {\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)] $, where $ a $ and $ b $ are constants. This is easy to plot, however, I want the angles $ \theta $ and $ \phi $ to satisfy an implicit equation, say, $ \cos\theta + a(\phi + b t)^2 + c = 0 $.

I am trying to plot a function $ {\bf x}(t) = r(t)\hat{v} + {\bf b}(t) $, with unit vector $ \hat{v} $ and vector $ {\bf b}(t) $ given in spherical coordinates. For simplicity, assume that $ \hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta) $, and $ {\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)] $, where $ a $ and $ b $ are constants. This is easy to plot, however, I want the angles $ \theta $ and $ \phi $ to satisfy an implicit equation, say, $ \cos\theta + a(\phi + b t)^2 + c = 0 $.

2 deleted 36 characters in body
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I am trying to plot a function $ {\bf x}(t) = a(t)\hat{v} + {\bf b}(t) $, with unit vector $ \hat{v} $ and vector $ {\bf b}(t) $ given in spherical coordinates. For simplicity, assume that $ \hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta) $, and $ {\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)] $, where $ a $ and $ b $ are constants. This is easy to plot, however, I want the angles $ \theta $ and $ \phi $ to satisfy an implicit equation, say, $ \cos\theta + a(\phi + b t)^2 + c = 0 $.

Thanks in advance for your help.

I am trying to plot a function $ {\bf x}(t) = a(t)\hat{v} + {\bf b}(t) $, with unit vector $ \hat{v} $ and vector $ {\bf b}(t) $ given in spherical coordinates. For simplicity, assume that $ \hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta) $, and $ {\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)] $, where $ a $ and $ b $ are constants. This is easy to plot, however, I want the angles $ \theta $ and $ \phi $ to satisfy an implicit equation, say, $ \cos\theta + a(\phi + b t)^2 + c = 0 $.

Thanks in advance for your help.

I am trying to plot a function $ {\bf x}(t) = a(t)\hat{v} + {\bf b}(t) $, with unit vector $ \hat{v} $ and vector $ {\bf b}(t) $ given in spherical coordinates. For simplicity, assume that $ \hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta) $, and $ {\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)] $, where $ a $ and $ b $ are constants. This is easy to plot, however, I want the angles $ \theta $ and $ \phi $ to satisfy an implicit equation, say, $ \cos\theta + a(\phi + b t)^2 + c = 0 $.

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Parametric 3D plot with parameters satisfying an implicit equation

I am trying to plot a function $ {\bf x}(t) = a(t)\hat{v} + {\bf b}(t) $, with unit vector $ \hat{v} $ and vector $ {\bf b}(t) $ given in spherical coordinates. For simplicity, assume that $ \hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta) $, and $ {\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)] $, where $ a $ and $ b $ are constants. This is easy to plot, however, I want the angles $ \theta $ and $ \phi $ to satisfy an implicit equation, say, $ \cos\theta + a(\phi + b t)^2 + c = 0 $.

Thanks in advance for your help.