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ARCH 689 Parametric Modeling in Architecture Vector Mathematics: Applications

ARCH 689 Parametric Modeling in Architecture Vector Mathematics: Applications. Wei Yan, Ph.D. Associate Professor Department of Architecture Texas A&M University. Use of Dot Product. Extract the projection.

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ARCH 689 Parametric Modeling in Architecture Vector Mathematics: Applications

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  1. ARCH 689 Parametric Modeling in ArchitectureVector Mathematics:Applications Wei Yan, Ph.D. Associate Professor Department of Architecture Texas A&M University

  2. Use of Dot Product

  3. Extract the projection • The dot product between the unit x vector (1,0,0) and a vector Vgives the component of Vin the x-direction.

  4. Work out the angle between 2 vectors cos(theta) = a.b/ (|a||b|) = (a1*b1 + a2*b2 + a3*b3) / (sqrt(a12+ a22 +a32) * sqrt(b12 + b22 +b32))

  5. The Dot Product measures the 'Right-Angularity' of 2 vectors • Vectors a and b are orthogonal if, and only if, a.b= 0.

  6. Use of Cross Product

  7. Cross product of 2 vectors, results in 3rd vector which is perpendicular to both of them. • For finding surface normal

  8. |a x b| = |a||b|sin(theta) = base * height • The length of the cross product is the area of the parallelogram made by the two vectors.

  9. Use of vectors • Many problems can be solved most easily by using vector operations. (And some problems can't really be expressed very well, without reference to vector operations.) • Geometry: find normal, find average direction of two lines, find projection, … • Physics: velocity, force

  10. General Tools • http://www.wolframalpha.com/input/?i=vector+%281%2C+2%2C+6%29+%2B+%284%2C+5%2C+3%29

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