OpenGL Mathematics
GLSL + Optional features = OpenGL Mathematics (GLM)
A C++ mathematics library for graphics programming


Compute a triangle normal:
  • #include <glm/glm.hpp>
  • void computeNormal(triangle & Triangle)
  • {
  • glm::vec3 const & a = Triangle.Position[0];
  • glm::vec3 const & b = Triangle.Position[1];
  • glm::vec3 const & c = Triangle.Position[2];
  • Triangle.Normal = glm::normalize(glm::cross(c - a, b - a));
  • }
Matrix transform:
  • // glm::vec3, glm::vec4, glm::ivec4, glm::mat4
  • #include <glm/glm.hpp>
  • // glm::translate, glm::rotate, glm::scale, glm::perspective
  • #include <glm/gtc/matrix_transform.hpp>
  • // glm::value_ptr
  • #include <glm/gtc/type_ptr.hpp>
  • {
  • glm::mat4 Projection =
  • glm::perspective(45.0f, 4.0f / 3.0f, 0.1f, 100.f);
  • glm::mat4 ViewTranslate = glm::translate(
  • glm::mat4(1.0f),
  • glm::vec3(0.0f, 0.0f, -Translate));
  • glm::mat4 ViewRotateX = glm::rotate(
  • ViewTranslate,
  • Rotate.y, glm::vec3(-1.0f, 0.0f, 0.0f));
  • glm::mat4 View = glm::rotate(
  • ViewRotateX,
  • Rotate.x, glm::vec3(0.0f, 1.0f, 0.0f));
  • glm::mat4 Model = glm::scale(
  • glm::mat4(1.0f),
  • glm::vec3(0.5f));
  • glm::mat4 MVP = Projection * View * Model;
  • glUniformMatrix4fv(
  • LocationMVP, 1, GL_FALSE, glm::value_ptr(MVP));
  • }
Vector types:
  • #include <glm/glm.hpp>
  • #include <glm/gtx/type_precision.hpp>
  • std::size_t const VertexCount = 4;
  • // Float quad geometry
  • std::size_t const PositionSizeF32 = VertexCount * sizeof(glm::vec2);
  • glm::vec2 const PositionDataF32[VertexCount] =
  • {
  • glm::vec2(-1.0f,-1.0f),
  • glm::vec2( 1.0f,-1.0f),
  • glm::vec2( 1.0f, 1.0f),
  • glm::vec2(-1.0f, 1.0f)
  • };
  • // Half-float quad geometry
  • std::size_t const PositionSizeF16 = VertexCount * sizeof(glm::hvec2);
  • glm::hvec2 const PositionDataF16[VertexCount] =
  • {
  • glm::hvec2(-1.0f, -1.0f),
  • glm::hvec2( 1.0f, -1.0f),
  • glm::hvec2( 1.0f, 1.0f),
  • glm::hvec2(-1.0f, 1.0f)
  • };
  • // 8 bits signed integer quad geometry
  • std::size_t const PositionSizeI8 = VertexCount * sizeof(glm::i8vec2);
  • glm::i8vec2 const PositionDataI8[VertexCount] =
  • {
  • glm::i8vec2(-1,-1),
  • glm::i8vec2( 1,-1),
  • glm::i8vec2( 1, 1),
  • glm::i8vec2(-1, 1)
  • };
  • // 32 bits signed integer quad geometry
  • std::size_t const PositionSizeI32 = VertexCount * sizeof(glm::i32vec2);
  • glm::i32vec2 const PositionDataI32[VertexCount] =
  • {
  • glm::i32vec2 (-1,-1),
  • glm::i32vec2 ( 1,-1),
  • glm::i32vec2 ( 1, 1),
  • glm::i32vec2 (-1, 1)
  • };
Lighting:
  • #include <glm/glm.hpp>
  • #include <glm/gtx/random.hpp>
  • glm::vec3 lighting
  • (
  • intersection const & Intersection,
  • material const & Material,
  • light const & Light,
  • glm::vec3 const & View
  • )
  • {
  • glm::vec3 Color = glm::vec3(0.0f);
  • glm::vec3 LightVertor = glm::normalize(
  • Light.position() - Intersection.globalPosition() +
  • glm::vecRand3(0.0f, Light.inaccuracy());
  • if(!shadow(
  • Intersection.globalPosition(),
  • Light.position(),
  • LightVertor))
  • {
  • float Diffuse = glm::dot(Intersection.normal(), LightVector);
  • if(Diffuse <= 0.0f)
  • return Color;
  • if(Material.isDiffuse())
  • Color += Light.color() * Material.diffuse() * Diffuse;
  • if(Material.isSpecular())
  • {
  • glm::vec3 Reflect = glm::reflect(
  • glm::normalize(-LightVector),
  • glm::normalize(Intersection.normal()));
  • float Dot = glm::dot(Reflect, View);
  • float Base = Dot > 0.0f ? Dot : 0.0f;
  • float Specular = glm::pow(Base, Material.exponent());
  • Color += Material.specular() * Specular;
  • }
  • }
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