Code archives/3D Graphics - Maths/Vector/Matrix Lib
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| V33 and a half. Added Gen_final_matrix..basically this totally simplifies the whole show, just use this to generate a transformation matrix, ePitch=20 eYaw=50 rRoll=0 X#=5 y#=5 z#=5 local tMatrix#[16] gen_final_matrix( ePitch,eYaw,eRoll,x,y,z,tMatrix) The result will be placed in tMatrix(Or whatever you call it, name is tied.) V1.1 Added functions to generate pitch/yaw/roll matrices and also a function to multiple two matrices by each other into a third output matrix(vital!) Basically to transform a point by a given pitch,yaw,roll as in blitz, do this, local pitchMatrix#[16],yawMatrix#[16],rollMatrix#[16] local tempMatrix#[16],finalMatrix#[16],positionMatrix#[16] gen_pitch_matrix( pitchMatrix,pitch) gen_yaw_matrix( yawMatrix,yaw) gen_roll_matrix( rollMatrix,roll) gen_position_matrix( positionMatrix,x,y,z) multi_mat( pitchMatrix,yawMatrix,tempMatrix) multi_mat( tempMatrix,rollMatrix,yawMatrix) multi_mat( rollMatrix,positionMatrix,finalMatrix) Now in final matrix you have a matrix that will transform any vector by the combined pitch/yaw/roll as expected. V1.0 - Perform matrice operations/transforms etc. There's also a tangent function in there to generate tangent space coords for normal/bump-mapping. Matrices are 16 element constant arrays. For example, local myMatrix[16] matrixIdentity( myMatrix) The reason being is there's no need to pass/collect the data, as the function works *directly* on the passed object. This is important for these type of mass use funcs... Also, vector(I.e 3 part variables) are 3 element constant arrays. i.e, local vectorA[3] myVectorFunc( vectorA) (btw I believe the triangle normal functions were culled from somewhere else..I know I didn't write them anyway, but definitely freeware..or I wouldn't have used them in the first place) | |||||
Function matrixIdentity(matrix#[16])
matrix[ 0] = 1.0; matrix[ 1] = 0.0; matrix[ 2] = 0.0; matrix[ 3] = 0.0;
matrix[ 4] = 0.0; matrix[ 5] = 1.0; matrix[ 6] = 0.0; matrix[ 7] = 0.0;
matrix[ 8] = 0.0; matrix[ 9] = 0.0; matrix[10] = 1.0; matrix[11] = 0.0;
matrix[12] = 0.0; matrix[13] = 0.0; matrix[14] = 0.0; matrix[15] = 1.0;
End Function
Function gen_pitch_matrix(matrix#[16])
matrix[0]=1:matrix[1]=0:matrix[2]=0:matrix[3]=0
matrix[4]=0:matrix[5]=Cos(a):matrix[6]=Sin(a):matrix[7]=0
matrix[8]=0:matrix[9]=-Sin(a):matrix[10]=Cos(a):matrix[11]=0
matrix[12]=0:matrix[13]=0:matrix[14]=0:matrix[15]=1
End Function
Function gen_yaw_mat(matrix#[16])
matrix[0]=Cos(a):matrix[1]=0:matrix[2]=-Sin(a):matrix[4]=0
matrix[4]=0:matrix[5]=1:matrix[6]=0:matrix[7]=0
matrix[8]=Sin(a):matrix[9]=0:matrix[10]=Cos(a):matrix[11]=0
matrix[12]=0:matrix[13]=0:matrix[14]=0:matrix[15]=0
End Function
Function gen_roll_matrix(matrix#[16])
matrix[0]=Cos(a):matrix[1]=Sin(a):matrix[2]=0:matrix[3]=0
matrix[4]=-Sin(a):matrix[5]=Cos(a):matrix[6]=0:matrix[7]=0
matrix[8]=0:matrix[9]=0:matrix[10]=0:matrix[11]=0
matrix[12]=0:matrix[13]=0:matrix[14]=0:matrix[15]=0
End Function
Function gen_position_matrix(matrix#[16],x#,y#,z#)
matrix[0]=1:matrix[1]=0:matrix[2]=0:matrix[3]=x
matrix[4]=0:matrix[5]=1:matrix[6]=0:matrix[7]=y
matrix[8]=0:matrix[9]=0:matrix[10]=0:matrix[11]=z
matrix[12]=0:matrix[13]=0:matrix[14]=0:matrix[15]=1
End Function
Function multi_mat(matrix1#[16],matrix2#[16],matrix3#[16]) ;Takes matrices i1 and i2 and combines them, resulting in i3
For m=0 To 3
For m1=0 To 3
matrix3[ m1*4+m]=0
For m2=0 To 3
matrix3[ m1*4+m]=matrix3[ m1*4+m1]+matrix2[m2*4+m]*matrix1[m1*4+m2]
Next
Next
Next
End Function
Function gen_final_matrix( pitch#,yaw#,roll#,x#,y#,z#,outMatrix#[16])
Local pitchMatrix#[16],yawMatrix#[16],rollMatrix#[16]
Local positionMatrix#[16],tempMatrix#[16]
gen_pitch_matrix( pitchMatrix,pitch)
gen_yaw_matrix( yawMatrix,yaw)
gen_roll_matrix( rollMatrix,roll)
gen_position_matrix( positionMatrix,x,y,z)
multi_mat(pitchMatrix,yawMatrix,tempMatrix)
multi_mat(tempMatrix,rollMatrix,pitchMatrix)
multi_mat(pitchMatrix,positionMatrix,outMatrix)
End Function
;//////////////////////////
;// Invert a matrix. (Matrix MUST be orhtonormal!)
;// in - Input matrix
;// out - Output matrix
;//////////////////////////
Function matrixInvert(in#[16], out#[16])
; // Transpose rotation
out[ 0] = in[ 0]; out[ 1] = in[ 4]; out[ 2] = in[ 8];
out[ 4] = in[ 1]; out[ 5] = in[ 5]; out[ 6] = in[ 9];
out[ 8] = in[ 2]; out[ 9] = in[ 6]; out[10] = in[10];
; // Clear shearing terms
out[3] = 0.0;f; out[7] = 0.0f; out[11] = 0.0f; out[15] = 1.0f;
; // Translation is minus the dot of tranlation And rotations
out[12] = -(in[12]*in[ 0]) - (in[13]*in[ 1]) - (in[14]*in[ 2]);
out[13] = -(in[12]*in[ 4]) - (in[13]*in[ 5]) - (in[14]*in[ 6]);
out[14] = -(in[12]*in[ 8]) - (in[13]*in[ 9]) - (in[14]*in[10]);
End Function
;//////////////////////////
;// Multiply a vector by a matrix.
;// vecIn - Input vector
;// m - Input matrix
;///////////////////////////
Function vecMatMult(vecIn#[3],m#[16], vecOut#[3])
vecOut[0] = (vecIn[0]*m[ 0]) + (vecIn[1]*m[ 4]) + (vecIn[2]*m[ 8]) + m[12];
vecOut[1] = (vecIn[0]*m[ 1]) + (vecIn[1]*m[ 5]) + (vecIn[2]*m[ 9]) + m[13];
vecOut[2] = (vecIn[0]*m[ 2]) + (vecIn[1]*m[ 6]) + (vecIn[2]*m[10]) + m[14];
End Function
;//////////////////////////
;// Multiply a vector by just the 3x3 portion of a matrix.
;// vecIn - Input vector
;// m - Input matrix
;// vecOut - Output vector
;//////////////////////////
;void
Function vecMat3x3Mult(vecIn#[3], m#[16], vecOut#[3])
vecOut[0] = (vecIn[0]*m[ 0]) + (vecIn[1]*m[ 4]) + (vecIn[2]*m[ 8]);
vecOut[1] = (vecIn[0]*m[ 1]) + (vecIn[1]*m[ 5]) + (vecIn[2]*m[ 9]);
vecOut[2] = (vecIn[0]*m[ 2]) + (vecIn[1]*m[ 6]) + (vecIn[2]*m[10]);
End Function
Function vecCrossProd (vecA#[3], vecB#[3], vecOut#[3])
vecOut[0] = vecA[1]*vecB[2] - vecA[2]*vecB[1];
vecOut[1] = vecA[2]*vecB[0] - vecA[0]*vecB[2];
vecOut[2] = vecA[0]*vecB[1] - vecA[1]*vecB[0];
End Function
Function vecNormalize#(vec#[3])
mag# = Sqr(vec[0]*vec[0] +vec[1]*vec[1] +vec[2]*vec[2]);
;// don't divide by zero
If (mag=0)
vec[0] = 0.0;f;
vec[1] = 0.0;f;
vec[2] = 0.0;f;
Return(0.0);
EndIf
vec[0] =vec[0]/mag;
vec[1] =vec[1]/mag;
vec[2] =vec[2]/mag;
Return(mag);
End Function
Function vecDotProd#(vecA#[3], vecB#[3])
Return(vecA[0]*vecB[0] +vecA[1]*vecB[1] +vecA[2]*vecB[2]);
End Function
Function vecCopy (vecIn#[3], vecOut#[3])
vecOut[0] = vecIn[0];
vecOut[1] = vecIn[1];
vecOut[2] = vecIn[2];
End Function
Function vector( v1#,v2#,v3#,vect#[3])
vect[0]=v1
vect[1]=v2
vect[2]=v3
End Function
Function tang( vertex#[3], vertex2#[3], vertex3#[3],texcoords#[2], texcoords2#[2], texcoords3#[2],polynormal#[3], tangent#[3], binormal#[3], normal#[3] )
Local txb#[3];
Local v1#[3],v2#[3]
VECTOR( vertex2[0] - vertex[0], texcoords2[0] - texcoords[0], texcoords2[1] - texcoords[1],v1 );
VECTOR( vertex3[0] - vertex[0], texcoords3[0] - texcoords[0], texcoords3[1] - texcoords[1],v2 );
crossProduct( v1, v2,txb );
If( Abs( txb[0] ) > EPSILON )
tangent[0] = -txb[1] / txb[0];
binormal[0] = -txb[2] / txb[0];
EndIf
v1[0] = vertex2[1] - vertex[1];
v2[0] = vertex3[1] - vertex[1];
CrossProduct( v1, v2,txb );
If( Abs( txb[0] ) > EPSILON )
tangent[1] = -txb[1] / txb[0];
binormal[1] = -txb[2] / txb[0];
EndIf
v1[0] = vertex2[2] - vertex[2];
v2[0] = vertex3[2] - vertex[2];
CrossProduct( v1, v2,txb);
If( Abs( txb[0] ) > EPSILON )
tangent[2] = -txb[1] / txb[0];
binormal[2] = -txb[2] / txb[0];
EndIf
Normalize( tangent );
Normalize( binormal );
;// Make a normal based on the tangent And binormal b/c it may be different than the poly's
;// normal, this normal being computed here is better
CrossProduct( tangent, binormal,normal);
Normalize( normal );
;// Make tangent space vectors orthogonal by recomputing the binormal with the corrected
;// tangent space normal.
CrossProduct( tangent, normal,biNormal);
Normalize( binormal );
If( vecDotProd( normal, polynormal ) < 0.0 )
normal[0] = -normal[0];
normal[1] = -normal[1];
normal[2] = -normal[2];
EndIf
End Function
Function TriangleNormal#(v1#[3],v2#[3],v3#[3],o#[3])
;SubVector v1,v2,
ux#=VectorX()
uy#=VectorY()
uz#=VectorZ()
;SubVector Cx#,Cy#,Cz#,Bx#,By#,Bz#
vx#=VectorX()
vy#=VectorY()
vz#=VectorZ()
;CrossProduct vx#,vy#,vz#,ux#,uy#,uz#
;Normalize vectorx,vectory,vectorz
;Return Ax#*vectorx+Ay#*vectory+Az#*vectorz
End Function
Function VectorX#()
Return vectorx
End Function
Function VectorY#()
Return vectory
End Function
Function VectorZ#()
Return vectorz
End Function
Function VectorW#()
Return vectorw
End Function
Function SubVector(v1#[3],v2#[3],o#[3])
o[0]=v1[0]-v2[0]
o[1]=v1[1]-v2[1]
o[2]=v1[2]=v2[2]
End Function
Function Normalize(v#[3])
If v[0]=0 And v[1]=0 And v[2]=0 Return
m#=Magnitude(v)
v[0]=v[0]/m#
v[1]=v[1]/m#
v[2]=v[2]/m#
End Function
Function CrossProduct(v1#[3],v2#[3],o#[3])
o[0]=v1[1]*v2[2]-v2[2]*v2[1]
o[1]=v1[2]*v2[0]-v1[0]*v2[2]
o[2]=v1[0]*v2[1]-v1[1]*v2[0]
End Function
Function Magnitude(v#[3])
Return Sqr( (v[0]*v[0]) + (v[1]*v[1]) + (v[2]*v[2]) )
End Function
Function TriangleNX#(surf,tri_no)
v0=TriangleVertex(surf,tri_no,0)
v1=TriangleVertex(surf,tri_no,1)
v2=TriangleVertex(surf,tri_no,2)
ax#=VertexX#(surf,v1)-VertexX#(surf,v0)
ay#=VertexY#(surf,v1)-VertexY#(surf,v0)
az#=VertexZ#(surf,v1)-VertexZ#(surf,v0)
bx#=VertexX#(surf,v2)-VertexX#(surf,v1)
by#=VertexY#(surf,v2)-VertexY#(surf,v1)
bz#=VertexZ#(surf,v2)-VertexZ#(surf,v1)
nx#=(ay#*bz#)-(az#*by#)
Return nx#
End Function
Function TriangleNY#(surf,tri_no)
v0=TriangleVertex(surf,tri_no,0)
v1=TriangleVertex(surf,tri_no,1)
v2=TriangleVertex(surf,tri_no,2)
ax#=VertexX#(surf,v1)-VertexX#(surf,v0)
ay#=VertexY#(surf,v1)-VertexY#(surf,v0)
az#=VertexZ#(surf,v1)-VertexZ#(surf,v0)
bx#=VertexX#(surf,v2)-VertexX#(surf,v1)
by#=VertexY#(surf,v2)-VertexY#(surf,v1)
bz#=VertexZ#(surf,v2)-VertexZ#(surf,v1)
ny#=(az#*bx#)-(ax#*bz#)
Return ny#
End Function
Function TriangleNZ#(surf,tri_no)
v0=TriangleVertex(surf,tri_no,0)
v1=TriangleVertex(surf,tri_no,1)
v2=TriangleVertex(surf,tri_no,2)
ax#=VertexX#(surf,v1)-VertexX#(surf,v0)
ay#=VertexY#(surf,v1)-VertexY#(surf,v0)
az#=VertexZ#(surf,v1)-VertexZ#(surf,v0)
bx#=VertexX#(surf,v2)-VertexX#(surf,v1)
by#=VertexY#(surf,v2)-VertexY#(surf,v1)
bz#=VertexZ#(surf,v2)-VertexZ#(surf,v1)
nz#=(ax#*by#)-(ay#*bx#)
Return nz#
End Function |
Comments
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| Well does gen_pitch_matrix() have one or two parameters? And where is gen_yaw_matrix? |
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| did you even test/use this matrix lib before you posted it here, or did you just write it down and put it here? the matrixIdentity function is crap as well. |
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| Riiiiight. Three year old math library and you're complaining to a banned user? |
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| HAHAHAHAHHHAH |
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| gen_yaw_matrix() is gen_yaw_mat(). Agreed, it's not very tidy code but what do you expect, it's free. I think it's pretty good code overall. |
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