Module: ObjParser::MathUtils

Defined in:
lib/obj_parser/math_utils.rb

Class Method Summary collapse

Class Method Details

.binormal2_for_vertices_and_texures(vertices, textures) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 29

def self.binormal2_for_vertices_and_texures(vertices, textures)
	u1, u2, u3 = textures.map {|texture| texture[0]}
	v1, v2, v3 = textures.map {|texture| texture[1]}
	p1, p2, p3 = vertices.map {|vertex| normalized_vector(vertex)}
	q1 = substract_vectors(p2, p1)
	q2 = substract_vectors(p3, p2)
	s1 = v2 - v1
	s2 = v3 - v1
	binormal = sum_vectors(mul_vector_by_scalar(q1, -s2), mul_vector_by_scalar(q2, s1))
end

.cross_product(v1, v2) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 40

def self.cross_product(v1, v2)
  [ ( (v1[1] * v2[2]) - (v1[2] * v2[1]) ),
   - ( (v1[0] * v2[2]) - (v1[2] * v2[0]) ),
     ( (v1[0] * v2[1]) - (v1[1] * v2[0]) ) ]
end

.divide_vector_by_scalar(vector, scalar) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 58

def self.divide_vector_by_scalar(vector, scalar)
  vector.map {|component|  component / scalar}
end

.dot(vector1, vector2) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 74

def self.dot(vector1, vector2)
	#http://en.wikipedia.org/wiki/Dot_product
	vector1.each_with_index.map do |component, index|
		component * vector2[index]
	end.inject(&:+)
end

.mat_inverse(mat) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 92

def self.mat_inverse(mat)
	m = Matrix[mat[0],mat[1], mat[2]]
	puts "non regular" unless m.regular?
	m.regular? ? m.inverse.to_a : m.to_a
end

.mul_mat_per_vector(mat, vector) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 86

def self.mul_mat_per_vector(mat, vector)
	m = Matrix[mat[0], mat[1], mat[2]]
	v = Matrix[ [vector[0]], [vector[1]], [vector[2]]]
	(m * v).to_a
end

.mul_vector_by_scalar(vector, scalar) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 54

def self.mul_vector_by_scalar(vector, scalar)
  vector.map {|component|  component * scalar}
end

.normal_for_face_with_vertices(face_vertices) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 98

def self.normal_for_face_with_vertices(face_vertices)
	p1 = face_vertices[0]
	p2 = face_vertices[1]
	p3 = face_vertices[2]
	u = substract_vectors(p2, p1)
	v = substract_vectors(p3, p1)
	cross_product(u, v)
end

.normalized_vector(vector) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 66

def self.normalized_vector(vector)
	current_vector_length = vector_length(vector)
	current_vector_length = current_vector_length == 0 ? 1 : current_vector_length
	vector.map do |component|
		component / current_vector_length
	end
end

.orthogonalized_vector_with_vector(vector1, vector2) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 81

def self.orthogonalized_vector_with_vector(vector1, vector2)
	#Gram-Schmidt orthogonalization -> http://jerome.jouvie.free.fr/opengl-tutorials/Lesson8.php
	substract_vectors(vector1, mul_vector_by_scalar(vector2, dot(vector2, vector1)))
end

.substract_vectors(a, b) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 46

def self.substract_vectors a, b
  [a[0] - b[0], a[1] - b[1], a[2] - b[2]]
end

.sum_vectors(a, b) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 50

def self.sum_vectors a, b
  [a[0] + b[0], a[1] + b[1], a[2] + b[2]]
end

.tangent2_for_vertices_and_texures(vertices, textures) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 18

def self.tangent2_for_vertices_and_texures(vertices, textures)
	u1, u2, u3 = textures.map {|texture| texture[0]}
	v1, v2, v3 = textures.map {|texture| texture[1]}
	p1, p2, p3 = vertices.map {|vertex| normalized_vector(vertex)}
	q1 = substract_vectors(p2, p1)
	q2 = substract_vectors(p3, p2)
	t1 = u2 - u1
	t2 = u3 - u1
	substract_vectors(mul_vector_by_scalar(q1, t2), mul_vector_by_scalar(q2, t1))
end

.tangent_for_vertices_and_texures(vertices, textures) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 7

def self.tangent_for_vertices_and_texures(vertices, textures)
	u1, u2, u3 = textures.map {|texture| texture[0]}
	v1, v2, v3 = textures.map {|texture| texture[1]}
	p1, p2, p3 = vertices.map {|vertex| normalized_vector(vertex)}
	#Tangent formula: http://jerome.jouvie.free.fr/opengl-tutorials/Lesson8.php
	nominator = substract_vectors( mul_vector_by_scalar(substract_vectors(p2, p1), (v3 - v1)), mul_vector_by_scalar(substract_vectors(p3, p1), (v2 - v1)))
	denominator = (u2 - u1) * (v3 - v1) - (v2 - v1) * (u3 - u1)
	denominator = denominator == 0 ? 1 : denominator
	divide_vector_by_scalar(nominator, denominator)
end

.vector_length(vector) ⇒ Object 



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# File 'lib/obj_parser/math_utils.rb', line 62

def self.vector_length(vector)
  Math.sqrt(vector.map { |item| (item * item) }.reduce(:+))
end