mathgl

func Ident2d ¶

func Ident2d() Mat2d

func Rotate2Dd ¶

func Rotate2Dd(angle float64) Mat2d

Rotate2D returns a rotation Matrix about a angle in 2-D space. Specifically about the origin. It is a 2x2 matrix, if you need a 3x3 for Homogeneous math (e.g. composition with a Translation matrix) see HomogRotate2D

func Ident2f ¶

func Ident2f() Mat2f

func Rotate2D ¶

func Rotate2D(angle float32) Mat2f

Rotate2D returns a rotation Matrix about a angle in 2-D space. Specifically about the origin. It is a 2x2 matrix, if you need a 3x3 for Homogeneous math (e.g. composition with a Translation matrix) see HomogRotate2D

func HomogRotate2Dd ¶

func HomogRotate2Dd(angle float64) Mat3d

Same as Rotate2D, except homogeneous (3x3 with the extra row/col being all zeroes with a one in the bottom right)

func Ident3d ¶

func Ident3d() Mat3d

func Rotate3DXd ¶

func Rotate3DXd(angle float64) Mat3d

Rotate3DX returns a 3x3 (non-homogeneous) Matrix that rotates by angle about the X-axis

Where c is cos(angle) and s is sin(angle)

[1 0 0]
[0 c -s]
[0 s c ]

func Rotate3DYd ¶

func Rotate3DYd(angle float64) Mat3d

Rotate3DY returns a 3x3 (non-homogeneous) Matrix that rotates by angle about the Y-axis

Where c is cos(angle) and s is sin(angle)

[c 0 s]
[0 1 0]
[s 0 c ]

func Rotate3DZd ¶

func Rotate3DZd(angle float64) Mat3d

Rotate3DZ returns a 3x3 (non-homogeneous) Matrix that rotates by angle about the Z-axis

Where c is cos(angle) and s is sin(angle)

[c -s 0]
[s c 0]
[0 0 1 ]

func Scale2Dd ¶

func Scale2Dd(scaleX, scaleY float64) Mat3d

Scale2D creates a homogeneous 2D scaling matrix [[ scaleX, 0 , 0 ]] [[ 0 , scaleY, 0 ]] [[ 0 , 0 , 1 ]]

func ShearX2Dd ¶

func ShearX2Dd(shear float64) Mat3d

ShearX2D creates a homogeneous 2D shear matrix along the X-axis

func ShearY2Dd ¶

func ShearY2Dd(shear float64) Mat3d

ShearY2D creates a homogeneous 2D shear matrix along the Y-axis

func Translate2Dd ¶

func Translate2Dd(Tx, Ty float64) Mat3d

Translate2D returns a homogeneous (3x3 for 2D-space) Translation matrix that moves a point by Tx units in the x-direction and Ty units in the y-direction

[[1, 0, Tx]]
[[0, 1, Ty]]
[[0, 0, 1 ]]

func HomogRotate2D ¶

func HomogRotate2D(angle float32) Mat3f

Same as Rotate2D, except homogeneous (3x3 with the extra row/col being all zeroes with a one in the bottom right)

func Ident3f ¶

func Ident3f() Mat3f

func Rotate3DX ¶

func Rotate3DX(angle float32) Mat3f

Rotate3DX returns a 3x3 (non-homogeneous) Matrix that rotates by angle about the X-axis

Where c is cos(angle) and s is sin(angle)

[1 0 0]
[0 c -s]
[0 s c ]

func Rotate3DY ¶

func Rotate3DY(angle float32) Mat3f

Rotate3DY returns a 3x3 (non-homogeneous) Matrix that rotates by angle about the Y-axis

Where c is cos(angle) and s is sin(angle)

[c 0 s]
[0 1 0]
[s 0 c ]

func Rotate3DZ ¶

func Rotate3DZ(angle float32) Mat3f

Rotate3DZ returns a 3x3 (non-homogeneous) Matrix that rotates by angle about the Z-axis

Where c is cos(angle) and s is sin(angle)

[c -s 0]
[s c 0]
[0 0 1 ]

func Scale2D ¶

func Scale2D(scaleX, scaleY float32) Mat3f

Scale2D creates a homogeneous 2D scaling matrix [[ scaleX, 0 , 0 ]] [[ 0 , scaleY, 0 ]] [[ 0 , 0 , 1 ]]

func ShearX2D ¶

func ShearX2D(shear float32) Mat3f

ShearX2D creates a homogeneous 2D shear matrix along the X-axis

func ShearY2D ¶

func ShearY2D(shear float32) Mat3f

ShearY2D creates a homogeneous 2D shear matrix along the Y-axis

func Translate2D ¶

func Translate2D(Tx, Ty float32) Mat3f

Translate2D returns a homogeneous (3x3 for 2D-space) Translation matrix that moves a point by Tx units in the x-direction and Ty units in the y-direction

[[1, 0, Tx]]
[[0, 1, Ty]]
[[0, 0, 1 ]]

func Frustumd ¶

func Frustumd(left, right, bottom, top, near, far float64) Mat4d

func HomogRotate3DXd ¶

func HomogRotate3DXd(angle float64) Mat4d

Same as Rotate3DX, except homogeneous (4x4 with the extra row/col being all zeroes with a one in the bottom right)

func HomogRotate3DYd ¶

func HomogRotate3DYd(angle float64) Mat4d

Same as Rotate3DY, except homogeneous (4x4 with the extra row/col being all zeroes with a one in the bottom right)

func HomogRotate3DZd ¶

func HomogRotate3DZd(angle float64) Mat4d

Same as Rotate3DZ, except homogeneous (4x4 with the extra row/col being all zeroes with a one in the bottom right)

func HomogRotate3Dd ¶

func HomogRotate3Dd(angle float64, axis Vec3d) Mat4d

HomogRotate3D creates a 3D rotation Matrix that rotates by (radian) angle about some arbitrary axis given by a Vector. It produces a homogeneous matrix (4x4)

Where c is cos(angle) and s is sin(angle), and x, y, and z are the first, second, and third elements of the axis vector (respectively):

[[ x^2(c-1)+c, xy(c-1)-zs, xz(c-1)+ys, 0 ]]
[[ xy(c-1)+zs, y^2(c-1)+c, yz(c-1)-xs, 0 ]]
[[ xz(c-1)-ys, yz(c-1)+xs, z^2(c-1)+c, 0 ]]
[[ 0         , 0         , 0         , 1 ]]

func Ident4d ¶

func Ident4d() Mat4d

func LookAtVd ¶

func LookAtVd(eye, center, up Vec3d) Mat4d

func LookAtd ¶

func LookAtd(eyeX, eyeY, eyeZ, centerX, centerY, centerZ, upX, upY, upZ float64) Mat4d

func Ortho2Dd ¶

func Ortho2Dd(left, right, top, bottom float64) Mat4d

Equivalent to Ortho with the near and far planes being -1 and 1, respectively

func Orthod ¶

func Orthod(left, right, bottom, top, near, far float64) Mat4d

func Perspectived ¶

func Perspectived(fovy, aspect, near, far float64) Mat4d

func Scale3Dd ¶

func Scale3Dd(scaleX, scaleY, scaleZ float64) Mat4d

Scale3D creates a homogeneous 3D scaling matrix [[ scaleX, 0 , 0 , 0 ]] [[ 0 , scaleY, 0 , 0 ]] [[ 0 , 0 , scaleZ, 0 ]] [[ 0 , 0 , 0 , 1 ]]

func ShearX3Dd ¶

func ShearX3Dd(shearY, shearZ float64) Mat4d

ShearX3D creates a homogeneous 3D shear matrix along the X-axis

func ShearY3Dd ¶

func ShearY3Dd(shearX, shearZ float64) Mat4d

ShearY3D creates a homogeneous 3D shear matrix along the Y-axis

func ShearZ3Dd ¶

func ShearZ3Dd(shearX, shearY float64) Mat4d

ShearZ3D creates a homogeneous 3D shear matrix along the Z-axis

func Translate3Dd ¶

func Translate3Dd(Tx, Ty, Tz float64) Mat4d

Translate3D returns a homogeneous (4x4 for 3D-space) Translation matrix that moves a point by Tx units in the x-direction, Ty units in the y-direction, and Tz units in the z-direction

[[1, 0, 0, Tx]]
[[0, 1, 0, Ty]]
[[0, 0, 1, Tz]]
[[0, 0, 0, 1 ]]

func Frustum ¶

func Frustum(left, right, bottom, top, near, far float32) Mat4f

func HomogRotate3D ¶

func HomogRotate3D(angle float32, axis Vec3f) Mat4f

HomogRotate3D creates a 3D rotation Matrix that rotates by (radian) angle about some arbitrary axis given by a Vector. It produces a homogeneous matrix (4x4)

Where c is cos(angle) and s is sin(angle), and x, y, and z are the first, second, and third elements of the axis vector (respectively):

[[ x^2(c-1)+c, xy(c-1)-zs, xz(c-1)+ys, 0 ]]
[[ xy(c-1)+zs, y^2(c-1)+c, yz(c-1)-xs, 0 ]]
[[ xz(c-1)-ys, yz(c-1)+xs, z^2(c-1)+c, 0 ]]
[[ 0         , 0         , 0         , 1 ]]

func HomogRotate3DX ¶

func HomogRotate3DX(angle float32) Mat4f

Same as Rotate3DX, except homogeneous (4x4 with the extra row/col being all zeroes with a one in the bottom right)

func HomogRotate3DY ¶

func HomogRotate3DY(angle float32) Mat4f

Same as Rotate3DY, except homogeneous (4x4 with the extra row/col being all zeroes with a one in the bottom right)

func HomogRotate3DZ ¶

func HomogRotate3DZ(angle float32) Mat4f

Same as Rotate3DZ, except homogeneous (4x4 with the extra row/col being all zeroes with a one in the bottom right)

func Ident4f ¶

func Ident4f() Mat4f

func LookAt ¶

func LookAt(eyeX, eyeY, eyeZ, centerX, centerY, centerZ, upX, upY, upZ float32) Mat4f

func LookAtV ¶

func LookAtV(eye, center, up Vec3f) Mat4f

func Ortho ¶

func Ortho(left, right, bottom, top, near, far float32) Mat4f

func Ortho2D ¶

func Ortho2D(left, right, top, bottom float32) Mat4f

Equivalent to Ortho with the near and far planes being -1 and 1, respectively

func Perspective ¶

func Perspective(fovy, aspect, near, far float32) Mat4f

func Scale3D ¶

func Scale3D(scaleX, scaleY, scaleZ float32) Mat4f

Scale3D creates a homogeneous 3D scaling matrix [[ scaleX, 0 , 0 , 0 ]] [[ 0 , scaleY, 0 , 0 ]] [[ 0 , 0 , scaleZ, 0 ]] [[ 0 , 0 , 0 , 1 ]]

func ShearX3D ¶

func ShearX3D(shearY, shearZ float32) Mat4f

ShearX3D creates a homogeneous 3D shear matrix along the X-axis

func ShearY3D ¶

func ShearY3D(shearX, shearZ float32) Mat4f

ShearY3D creates a homogeneous 3D shear matrix along the Y-axis

func ShearZ3D ¶

func ShearZ3D(shearX, shearY float32) Mat4f

ShearZ3D creates a homogeneous 3D shear matrix along the Z-axis

func Translate3D ¶

func Translate3D(Tx, Ty, Tz float32) Mat4f

Translate3D returns a homogeneous (4x4 for 3D-space) Translation matrix that moves a point by Tx units in the x-direction, Ty units in the y-direction, and Tz units in the z-direction

[[1, 0, 0, Tx]]
[[0, 1, 0, Ty]]
[[0, 0, 1, Tz]]
[[0, 0, 0, 1 ]]

func QuatIdentd ¶

func QuatIdentd() Quatd

func QuatLerpd ¶

func QuatLerpd(q1, q2 Quatd, amount float64) Quatd

func QuatNlerpd ¶

func QuatNlerpd(q1, q2 Quatd, amount float64) Quatd

func QuatRotated ¶

func QuatRotated(angle float64, axis Vec3d) Quatd

func QuatSlerpd ¶

func QuatSlerpd(q1, q2 Quatd, amount float64) Quatd

func QuatIdentf ¶

func QuatIdentf() Quatf

func QuatLerpf ¶

func QuatLerpf(q1, q2 Quatf, amount float32) Quatf

func QuatNlerpf ¶

func QuatNlerpf(q1, q2 Quatf, amount float32) Quatf

func QuatRotatef ¶

func QuatRotatef(angle float32, axis Vec3f) Quatf

func QuatSlerpf ¶

func QuatSlerpf(q1, q2 Quatf, amount float32) Quatf

func Projectd ¶

func Projectd(obj Vec3d, modelview, projection Mat4d, initialX, initialY, width, height int) (win Vec3d)

Transform a set of coordinates from object space (in obj) to window coordinates (with depth)

Window coordinates are continuous, not discrete (well, as continuous as an IEEE Floating Point can be), so you won't get exact pixel locations without rounding or similar

func UnProjectd ¶

func UnProjectd(win Vec3d, modelview, projection Mat4d, initialX, initialY, width, height int) (obj Vec3d, err error)

Transform a set of window coordinates to object space. If your MVP (projection.Mul(modelview) matrix is not invertible, this will return an error

Note that the projection may not be perfect if you use strict pixel locations rather than the exact values given by Projectf. (It's still unlikely to be perfect due to precision errors, but it will be closer)

func Projectf ¶

func Projectf(obj Vec3f, modelview, projection Mat4f, initialX, initialY, width, height int) (win Vec3f)

Transform a set of coordinates from object space (in obj) to window coordinates (with depth)

Window coordinates are continuous, not discrete (well, as continuous as an IEEE Floating Point can be), so you won't get exact pixel locations without rounding or similar

func UnProjectf ¶

func UnProjectf(win Vec3f, modelview, projection Mat4f, initialX, initialY, width, height int) (obj Vec3f, err error)

Transform a set of window coordinates to object space. If your MVP (projection.Mul(modelview) matrix is not invertible, this will return an error

Note that the projection may not be perfect if you use strict pixel locations rather than the exact values given by Projectf. (It's still unlikely to be perfect due to precision errors, but it will be closer)